Scholars@Duke
Guglielmo Scovazzi

Guglielmo Scovazzi CV

Professor in the Department of Civil and Environmental Engineering
Civil and Environmental Engineering
guglielmo.scovazzi@duke.edu
Box 90287, Durham, NC 27708
121 Hudson Hall, Box 90287, Durham, NC 27708
CV

Scholarly Works - Journal articles

A shifted interface approach for internal discontinuities in poroelastic media

Journal article Computers and Geotechnics · February 1, 2027 Porous media containing cracks, fractures, or internal discontinuities arise throughout subsurface geomechanics, biomechanics, and materials science. Numerical simulation of the coupled hydromechanical response is inherently challenging because the pressur ... Full text Cite

The Gap-Shifted Boundary Method for solid mechanics problems: Linear elasticity, hyperelasticity and elastoplasticity

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2026 Immersed finite element methods significantly alleviate the burden of body-fitted mesh generation for complex geometries, yet they frequently suffer from algorithmic complexities associated with cut-cell numerical integration and matrix ill-conditioning. T ... Full text Cite

The isogeometric Gap-Shifted Boundary Method

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2026 High-order immersed methods offer significant advantages for the simulation of complex geometries, but their practical performance is often limited by a trade-off between accuracy, robustness, and numerical conditioning. In this work, we present a high-ord ... Full text Cite

Phase-field/discontinuity capturing operator for direct van der waals simulation (DVS)

Journal article Journal of Computational Physics · June 1, 2026 Discontinuity capturing (DC) operators are commonly employed to numerically solve problems involving sharp gradients in the solution. Despite their success, the application of DC operators to the direct van der Waals simulation (DVS) remains challenging. T ... Full text Cite

Gap-SBM: A new conceptualization of the shifted boundary method with optimal convergence for the Neumann and Dirichlet problems

Journal article Computer Methods in Applied Mechanics and Engineering · May 1, 2026 We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the L2- and H1-norms of the error. The proposed method is built on t ... Full text Cite

The generalized shifted boundary method for geometry-parametric PDEs and time-dependent domains

Journal article Computer Methods in Applied Mechanics and Engineering · April 15, 2026 Many engineering and scientific problems require the solution of partial differential equations in complex geometries. Often, these problems involve parametrized geometries, e.g. design optimization, or moving domains, e.g. fluid-structure interaction prob ... Full text Cite

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

Journal article Computers and Mathematics with Applications · March 1, 2026 The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintaine ... Full text Cite

A weighted shifted boundary method for the Navier-Stokes equations with immersed moving boundaries

Journal article Journal of Computational Physics · March 1, 2026 The Weighted Shifted Boundary Method (WSBM) was recently introduced as an enhanced Shifted Boundary Method (SBM) for the simulation of flows with moving boundaries. Earlier work of the authors on no-slip boundary conditions for the two-dimensional Stokes f ... Full text Cite

A shifted boundary method for thermal flows

Journal article Journal of Computational Physics · February 15, 2026 We present an implementation of the Shifted Boundary Method (Octree-SBM) on incomplete Octree meshes for multiphysics simulations of coupled flow and heat transfer. Specifically, a semi-implicit formulation of the thermal Navier-Stokes equations is used to ... Full text Cite

Simulating incompressible flows over complex geometries using the shifted boundary method with incomplete adaptive octree meshes

Journal article Journal of Computational Physics · January 1, 2026 We extend the Shifted Boundary Method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids. Recently, octree grids ... Full text Cite

Direct flow simulations with implicit neural representation of complex geometry

Journal article Computer Methods in Applied Mechanics and Engineering · November 1, 2025 Implicit neural representations (e.g., neural network-based signed distance fields) have emerged as a powerful approach for encoding complex geometries as continuous functions. These implicit models are widely used in computer vision and 3D content creatio ... Full text Cite

OCTREE-BASED ADAPTIVE MESH REFINEMENT AND THE SHIFTED BOUNDARY METHOD FOR EFFICIENT FLUID DYNAMICS SIMULATIONS

Journal article Advances in Computational Science and Engineering · June 1, 2025 This paper presents an adaptive mesh refinement (AMR) framework integrated with the shifted boundary method (SBM) for incompressible flow and coupled thermal-flow simulations. Our framework leverages octreebased AMR, enabling hierarchical and dynamic mesh ... Full text Cite

The Shifted Boundary Method for contact problems

Journal article Computer Methods in Applied Mechanics and Engineering · May 15, 2025 We propose an embedded algorithm for contact mechanics based on the Shifted Boundary Method. The contact conditions are applied on a surrogate contact surface in proximity of the true contact surface and Taylor expansions are used to change (shift) both th ... Full text Cite

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Journal article Journal of Computational Physics · February 15, 2025 We present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the ... Full text Cite

A Shifted Boundary Method for the compressible Euler equations

Journal article Journal of Computational Physics · January 1, 2025 The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the asso ... Full text Cite

Crack branching and merging simulations with the shifted fracture method

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2025 We propose a relatively simple and mesh-independent approach to model crack branching and merging using the Shifted Fracture Method (SFM), within the class of Shifted Boundary Methods. The proposed method achieves mesh independency by accurately accounting ... Full text Cite

The Shifted Boundary Method in Isogeometric Analysis

Journal article Computer Methods in Applied Mechanics and Engineering · October 1, 2024 This work presents a novel application of the Shifted Boundary Method (SBM) within the Isogeometric Analysis (IGA) framework, applying it to two-dimensional and three-dimensional Poisson problems with Dirichlet and Neumann boundary conditions. The SBM boun ... Full text Cite

A weighted shifted boundary method for immersed moving boundary simulations of Stokes' flow

Journal article Journal of Computational Physics · August 1, 2024 The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain ... Full text Cite

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Journal article Journal of Computational Physics · June 15, 2024 We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the va ... Full text Cite

Nonlinear elasticity with the Shifted Boundary Method

Journal article Computer Methods in Applied Mechanics and Engineering · June 1, 2024 We propose a new unfitted/immersed computational framework for nonlinear solid mechanics, which bypasses the complexities associated with the generation of CAD representations and subsequent body-fitted meshing. This approach allows to speed up the cycle o ... Full text Cite

Mixed Averaging Procedures

Journal article Flow Turbulence and Combustion · April 1, 2024 The statistical operators typically applied in postprocessing numerical databases for statistically steady turbulence are a mixture of physical averages in homogeneous spatial directions and in time. Alternative averaging operators may involve phase or ens ... Full text Cite

A shifted boundary method based on extension operators

Journal article Computer Methods in Applied Mechanics and Engineering · March 1, 2024 We consider formulations of the Shifted Boundary Method based on extrapolation operators other than the Taylor expansion. In the specific case of the Poisson equation, we prove that this approach is stable, provided some basic properties of well-posedness ... Full text Cite

Optimal surrogate boundary selection and scalability studies for the shifted boundary method on octree meshes

Journal article Computer Methods in Applied Mechanics and Engineering · February 1, 2024 The accurate and efficient simulation of Partial Differential Equations (PDEs) in and around arbitrarily defined geometries is critical for many application domains. Immersed boundary methods (IBMs) alleviate the usually laborious and time-consuming proces ... Full text Cite

Complex-geometry simulations of transient thermoelasticity with the Shifted Boundary Method

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2024 We propose a formulation of the Shifted Boundary Method, an immersed/embedded/unfitted boundary method, for transient thermo-elasticity problems characterized by very complex geometries. With an extensive set of numerical experiments, we demonstrate that t ... Full text Cite

A penalty-free Shifted Boundary Method of arbitrary order

Journal article Computer Methods in Applied Mechanics and Engineering · December 15, 2023 We introduce and analyze a penalty-free formulation of the Shifted Boundary Method (SBM), inspired by the asymmetric version of the Nitsche method. We prove its stability and convergence for arbitrary order finite element interpolation spaces and we test i ... Full text Cite

A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity

Journal article Computer Methods in Applied Mechanics and Engineering · July 1, 2023 We propose a stabilized linear tetrahedral finite element method for static, finite elasticity problems involving compressible and nearly incompressible materials. Our approach relies on a mixed formulation, in which the nodal displacement unknown filed is ... Full text Cite

The simple shifted fracture method

Journal article International Journal for Numerical Methods in Engineering · June 30, 2023 We propose a simplified version of the Shifted Fracture Method (SFM), which relies on an approximate fracture geometry representation combined with approximate interface conditions. In particular, we show that the complexities of earlier SFM implementation ... Full text Cite

A blended shifted-fracture/phase-field framework for sharp/diffuse crack modeling

Journal article International Journal for Numerical Methods in Engineering · February 28, 2023 The shifted fracture method (SFM) is an embedded method that enables sharp crack representations while using mesh-fitted data structures. In the SFM, the true crack is embedded in the computational grid, but the crack interface conditions are approximated ... Full text Cite

Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method

Journal article Computer Methods in Applied Mechanics and Engineering · August 1, 2022 We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary Method for spatial di ... Full text Cite

The high-order Shifted Boundary Method and its analysis

Journal article Computer Methods in Applied Mechanics and Engineering · May 1, 2022 The Shifted Boundary Method (SBM) is an approximate domain method for boundary value problems, in the broader class of unfitted/embedded/immersed methods, that has proven efficient in handling partial differential equation problems with complex geometries. ... Full text Cite

The shifted fracture method

Journal article International Journal for Numerical Methods in Engineering · November 30, 2021 We propose a new framework for fracture mechanics, based on the idea of an approximate fracture geometry representation combined with approximate interface conditions. Our approach evolves from the shifted interface method, and introduces the concept of an ... Full text Cite

The shifted boundary method for solid mechanics

Journal article International Journal for Numerical Methods in Engineering · October 30, 2021 We propose a new embedded/immersed framework for computational solid mechanics, aimed at vastly speeding up the cycle of design and analysis in complex geometry. In many problems of interest, our approach bypasses the complexities associated with the gener ... Full text Cite

Analysis Of The Shifted Boundary Method For The Poisson Problem In Domains With Corners

Journal article Mathematics of Computation · September 1, 2021 The shifted boundary method (SBM) is an approximate domain method for boundary value problems, in the broader class of unfitted/embedded/immersed methods. It has proven to be quite efficient in handling problems with complex geometries, ranging from Poisso ... Full text Cite

A blended transient/quasistatic Lagrangian framework for salt tectonics simulations with stabilized tetrahedral finite elements

Journal article International Journal for Numerical Methods in Engineering · July 30, 2021 We propose a Lagrangian solid mechanics framework for the simulation of salt tectonics and other large-deformation geomechanics problems at the basin scale. Our approach relies on general elastic-viscoplastic constitutive models to characterize the deforma ... Full text Cite

A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity

Journal article Mechanics Research Communications · March 1, 2021 We present a computational approach to solve problems in multiplicative nonlinear viscoelasticity using piecewise linear finite elements on triangular and tetrahedral grids, which are very versatile for simulations in complex geometry. Our strategy is base ... Full text Cite

A weighted Shifted Boundary Method for free surface flow problems

Journal article Journal of Computational Physics · January 1, 2021 The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By ... Full text Cite

The second-generation Shifted Boundary Method and its numerical analysis

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2020 Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoid ... Full text Cite

A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

Journal article Computer Methods in Applied Mechanics and Engineering · October 1, 2020 We investigate a projection-based reduced order model of the steady incompressible Navier–Stokes equations for moderate Reynolds numbers. In particular, we construct an “embedded” reduced basis space, by applying proper orthogonal decomposition to the Shif ... Full text Cite

The Shifted Interface Method: A flexible approach to embedded interface computations

Journal article International Journal for Numerical Methods in Engineering · February 15, 2020 We propose a new embedded finite element method to simulate partial differential equations over domains with internal interfaces. Our approach belongs to the family of surrogate/approximate interface methods and relies on the idea of shifting the location ... Full text Cite

Analysis of the shifted boundary method for the Stokes problem

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2020 The analysis of stability and accuracy of the shifted boundary method is developed for the Stokes flow equations. The key feature of the shifted boundary method, an embedded finite element method, is the shifting of the location where boundary conditions a ... Full text Cite

High-order gradients with the shifted boundary method: An embedded enriched mixed formulation for elliptic PDEs

Journal article Journal of Computational Physics · December 1, 2019 We propose an extension of the embedded boundary method known as “shifted boundary method” to elliptic diffusion equations in mixed form (e.g., Darcy flow, heat diffusion problems with rough coefficients, etc.). Our aim is to obtain an improved formulation ... Full text Cite

An ALE/embedded boundary method for two-material flow simulations

Journal article Computers and Mathematics with Applications · July 15, 2019 We present a computational framework that combines an embedded boundary method and an arbitrary Lagrangian–Eulerian (ALE) method for multi-material flow computations of compressible fluids. The methodology is presented for two-material flows and one-materi ... Full text Cite

A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow

Journal article Computer Methods in Applied Mechanics and Engineering · April 15, 2019 We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to deal with complex parametrized domains in an efficient and straightforward way. The impact of the proposed appr ... Full text Cite

On the robustness of variational multiscale error estimators for the forward propagation of uncertainty

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2018 The numerical simulation of physical phenomena and engineering problems can be affected by numerical errors and various types of uncertainties. Characterizing the former in computational frameworks involving system parameter uncertainties becomes a key iss ... Full text Cite

The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems

Journal article Journal of Computational Physics · November 1, 2018 We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms. The key feature of the proposed approach is the idea of shifting the location where boundary conditions are a ... Full text Cite

The shifted boundary method for embedded domain computations. Part II: Linear advection–diffusion and incompressible Navier–Stokes equations

Journal article Journal of Computational Physics · November 1, 2018 We propose a new embedded finite element method for the linear advection–diffusion equation and the laminar and turbulent incompressible Navier–Stokes equations. The proposed method belongs to the class of surrogate/approximate boundary algorithms and is b ... Full text Cite

The shifted boundary method for hyperbolic systems: Embedded domain computations of linear waves and shallow water flows

Journal article Journal of Computational Physics · September 15, 2018 We propose a new computational approach for embedded boundary simulations of hyperbolic systems and, in particular, the linear wave equations and the nonlinear shallow water equations. The proposed approach belongs to the class of surrogate/approximate bou ... Full text Cite

Elastoplasticity with linear tetrahedral elements: A variational multiscale method

Journal article International Journal for Numerical Methods in Engineering · August 24, 2018 We present a computational framework for the simulation of J2-elastic/plastic materials in complex geometries based on simple piecewise linear finite elements on tetrahedral grids. We avoid spurious numerical instabilities by means of a specific ... Full text Cite

Dual-scale Galerkin methods for Darcy flow

Journal article Journal of Computational Physics · February 1, 2018 The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computat ... Full text Cite

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

Journal article Journal of Computational Physics · February 1, 2018 Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian method ... Full text Cite

A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements

Journal article International Journal for Numerical Methods in Engineering · December 28, 2017 In this article, we develop a dynamic version of the variational multiscale (D-VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The constitutive models considered here are based on Prony series expans ... Full text Cite

A velocity/stress mixed stabilized nodal finite element for elastodynamics: Analysis and computations with strongly and weakly enforced boundary conditions

Journal article Computer Methods in Applied Mechanics and Engineering · October 1, 2017 A new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain. Our method is based on equal-order interpolation discrete spaces for both the velocity (or displacement) and stress (or s ... Full text Cite

Analytical and variational numerical methods for unstable miscible displacement flows in porous media

Journal article Journal of Computational Physics · April 15, 2017 The miscible displacement of one fluid by another in a porous medium has received considerable attention in subsurface, environmental and petroleum engineering applications. When a fluid of higher mobility displaces another of lower mobility, unstable patt ... Full text Cite

Implicit finite incompressible elastodynamics with linear finite elements: A stabilized method in rate form

Journal article Computer Methods in Applied Mechanics and Engineering · November 1, 2016 We propose a stabilization method for linear tetrahedral finite elements, suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics. In particular, we derive and discuss a generalized framework ... Full text Cite

A variational multiscale finite element method for monolithic ALE computations of shock hydrodynamics using nodal elements

Journal article Journal of Computational Physics · June 15, 2016 We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations ... Full text Cite

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach

Journal article International Journal for Numerical Methods in Engineering · June 8, 2016 We propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by ... Full text Cite

A Nitsche method for wave propagation problems in time domain

Journal article Computer Methods in Applied Mechanics and Engineering · August 5, 2015 We propose a new Nitsche-type approach for the weak enforcement of Dirichlet and Neumann boundary conditions in the context of time-domain wave propagation problems in mixed form. A peculiar feature of the proposed method is that, due to the hyperbolic str ... Full text Cite

Algebraic multigrid techniques for discontinuous Galerkin methods with varying polynomial order

Journal article Computational Geosciences · September 1, 2014 We present a parallel algebraic multigrid (AMG) algorithm for the implicit solution of the Darcy problem discretized by the discontinuous Galerkin (DG) method that scales optimally for regular and irregular meshes. The main idea centers on recasting the pr ... Full text Cite

A frame-invariant vector limiter for flux corrected nodal remap in arbitrary Lagrangian-Eulerian flow computations

Journal article Journal of Computational Physics · August 1, 2014 This article describes a frame-invariant vector limiter for Flux-Corrected Transport (FCT) numerical methods. Our approach relies on an objective vector projection, and, because of its intrinsic structure, the proposed approach can be generalized with ease ... Full text Cite

A fully-coupled upwind discontinuous Galerkin method for incompressible porous media flows: High-order computations of viscous fingering instabilities in complex geometry

Journal article Journal of Computational Physics · November 1, 2013 We present a new approach to the simulation of viscous fingering instabilities in incompressible, miscible displacement flows in porous media. In the past, high resolution computational simulations of viscous fingering instabilities have always been perfor ... Full text Cite

A high resolution Lagrangian method using nonlinear hybridization and hyperviscosity

Journal article Computers and Fluids · August 6, 2013 Classical artificial viscosity methods often suffer from excessive numerical viscosity both at and away from shocks. While a proper amount of dissipation is necessary at the shock wave, it should be minimized away from the shock and disappear where the flo ... Full text Cite

A high-order, fully coupled, upwind, compact discontinuous Galerkin method for modeling of viscous fingering in compressible porous media

Journal article Computer Methods in Applied Mechanics and Engineering · August 5, 2013 We present a new approach for high-fidelity compressible porous media simulations. Our method is based on a fully coupled, upwind, high-order discontinuous Galerkin formulation of the equations of miscible displacement transport. A key feature of the propo ... Full text Cite

Isogeometric analysis of Lagrangian hydrodynamics

Journal article Journal of Computational Physics · June 5, 2013 Isogeometric analysis of Lagrangian shock hydrodynamics is proposed. The Euler equations of compressible hydrodynamics in the weak form are discretized using Non-Uniform Rational B-Splines (NURBS) in space. The discretization has all the advantages of a hi ... Full text Cite

Computing gravity-driven viscous fingering in complex subsurface geometries: A high-order discontinuous Galerkin approach

Journal article Computational Geosciences · April 1, 2013 We present a formulation of the discontinuous Galerkin method aimed for simulations of gravity-driven viscous fingering instabilities occurring in porous media flow. Specifically, we are targeting applications characterized by complex geometrical features. ... Full text Cite

A discontinuous galerkin method for gravity-driven viscous fingering instabilities in porous media

Journal article Journal of Computational Physics · January 1, 2013 We present a new approach to the simulation of gravity-driven viscous fingering instabilities in porous media flow. These instabilities play a very important role during carbon sequestration processes in brine aquifers. Our approach is based on a nonlinear ... Cite

Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach

Journal article Journal of Computational Physics · October 15, 2012 In the past, a number of attempts have failed to robustly compute highly transient shock hydrodynamics flows on tetrahedral meshes. To a certain degree, this is not a surprise, as prior attempts emphasized enhancing the structure of shock-capturing operato ... Full text Cite

Weak boundary conditions for wave propagation problems in confined domains: Formulation and implementation using a variational multiscale method

Journal article Computer Methods in Applied Mechanics and Engineering · May 1, 2012 We propose a new approach to the enforcement of Dirichlet, Neumann, or Robin boundary conditions in finite element computations of wave propagation problems. The key idea is to enforce the boundary conditions weakly as part of the variational formulation. ... Full text Cite

A discontinuous Galerkin method for gravity-driven viscous fingering instabilities in porous media

Journal article Journal of Computational Physics · 2012 We present a new approach to the simulation of gravity-driven viscous fingering instabilities in porous media flow. These instabilities play a very important role during carbon sequestration processes in brine aquifers. Our approach is based on a nonlinear ... Full text Cite

Numerical methods for multi-material fluids and structures (MULTIMAT-2009)

Journal article International Journal for Numerical Methods in Fluids · April 1, 2011 Full text Cite

A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian-Eulerian computations with nodal finite elements

Journal article Journal of Computational Physics · January 1, 2011 This article describes a conservative synchronized remap algorithm applicable to arbitrary Lagrangian-Eulerian computations with nodal finite elements. In the proposed approach, ideas derived from flux-corrected transport (FCT) methods are extended to cons ... Full text Cite

Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian-Eulerian methods

Journal article Journal of Computational Physics · January 1, 2011 We develop and study the high-order conservative and monotone optimization-based remap (OBR) of a scalar conserved quantity (mass) between two close meshes with the same connectivity. The key idea is to phrase remap as a global inequality-constrained optim ... Full text Cite

A heterogeneous multiscale modeling framework for hierarchical systems of partial differential equations

Journal article International Journal for Numerical Methods in Fluids · January 1, 2011 This paper presents a heterogeneous multiscale method with efficient interscale coupling for scale-dependent phenomena modeled via a hierarchy of partial differential equations. Physics at the global level is governed by one set of partial differential equ ... Full text Cite

A conservative nodal variational multiscale method for Lagrangian shock hydrodynamics

Journal article Computer Methods in Applied Mechanics and Engineering · December 15, 2010 A new method based on a continuous, piece-wise linear approximation of the equations for Lagrangian shock hydrodynamics is presented. Numerical instabilities are controlled by a stabilizing operator derived using the paradigm of the variational multiscale ... Full text Cite

A generalized view on Galilean invariance in stabilized compressible flow computations

Journal article International Journal for Numerical Methods in Fluids · December 7, 2010 This article presents a generalized analysis on the significance of Galilean invariance in compressible flow computations with stabilized and variational multi-scale methods. The understanding of the key issues and the development of general approaches to ... Full text Cite

Stabilized methods for compressible flows

Journal article Journal of Scientific Computing · January 1, 2010 This article reviews 25 years of research of the authors and their collaborators on stabilized methods for compressible flow computations. An historical perspective is adopted to document the main advances from the initial developments to modern approaches ... Full text Cite

Stability analysis of a predictor/multi-corrector method for staggered-grid Lagrangian shock hydrodynamics

Journal article Journal of Computational Physics · November 1, 2009 This article presents the complete von Neumann stability analysis of a predictor/multi-corrector scheme derived from an implicit mid-point time integrator often used in shock hydrodynamics computations in combination with staggered spatial discretizations. ... Full text Cite

On the angular momentum conservation and incremental objectivity properties of a predictor/multi-corrector method for Lagrangian shock hydrodynamics

Journal article Computer Methods in Applied Mechanics and Engineering · September 1, 2009 This article presents an analysis of the global angular momentum conservation and objectivity properties for a predictor/multi-corrector scheme often used in shock hydrodynamics computations in combination with staggered spatial discretizations. As the num ... Full text Cite

Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations

Journal article Computer Methods in Applied Mechanics and Engineering · February 1, 2008 A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradig ... Full text Cite

ALEGRA: An arbitrary Lagrangian-Eulerian multimaterial, multiphysics code

Journal article 46th AIAA Aerospace Sciences Meeting and Exhibit · January 1, 2008 ALEGRA is an arbitrary Lagrangian-Eulerian (multiphysics) computer code developed at Sandia National Laboratories since 1990. The code contains a variety of physics options including magnetics, radiation, and multimaterial flow. The code has been developed ... Full text Cite

Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows

Journal article Computer Methods in Applied Mechanics and Engineering · December 1, 2007 We present an LES-type variational multiscale theory of turbulence. Our approach derives completely from the incompressible Navier-Stokes equations and does not employ any ad hoc devices, such as eddy viscosities. We tested the formulation on forced homoge ... Full text Cite

Galilean invariance and stabilized methods for compressible flows

Journal article International Journal for Numerical Methods in Fluids · July 20, 2007 In a recent work (Comput. Methods Appl. Mech. Eng. 2007; 196(4-6):966-978), it was observed that lack of Galilean invariance led to catastrophic instabilities when stabilized methods were used in Lagrangian shock hydrodynamics computations. By means of an ... Full text Cite

Stabilized shock hydrodynamics: II. Design and physical interpretation of the SUPG operator for Lagrangian computations

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2007 A new SUPG-stabilized formulation for Lagrangian Hydrodynamics of materials satisfying the Mie-Grüneisen equation of state was presented in the first paper of the series [G. Scovazzi, M.A. Christon, T.J.R. Hughes, J.N. Shadid, Stabilized shock hydrodynamic ... Full text Cite

A discourse on Galilean invariance, SUPG stabilization, and the variational multiscale framework

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2007 Galilean invariance is one of the key requirements of many physical models adopted in theoretical and computational mechanics. Spurred by recent research developments in shock hydrodynamics computations [G. Scovazzi, Stabilized shock hydrodynamics: II. Des ... Full text Cite

Stabilized shock hydrodynamics: I. A Lagrangian method

Journal article Computer Methods in Applied Mechanics and Engineering · January 1, 2007 A new SUPG-stabilized formulation for Lagrangian hydrodynamics of materials satisfying Mie-Grüneisen equation of state is proposed. It allows the use of simplex-type (triangular/tetrahedral) meshes as well as the more commonly used brick-type (quadrilatera ... Full text Cite

A multiscale discontinuous Galerkin method

Journal article Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics · June 29, 2006 We propose a new class of Discontinuous Galerkin (DG) methods based on variational multiscale ideas. Our approach begins with an additive decomposition of the discontinuous finite element space into continuous (coarse) and discontinuous (fine) components, ... Full text Cite

A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method

Journal article Computer Methods in Applied Mechanics and Engineering · April 1, 2006 Proliferation of degrees-of-freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data struct ... Full text Cite