Georg May

Journal Article Journal of Computational Physics · November 1, 2025 In the context of increasing interest in space exploration, having a reliable means of predicting the behaviour of thermal protection material during atmospheric re-entry is of capital importance. Inductively coupled plasma facilities have been designed to ... Full text Cite

Towards a robust time-accurate anisotropically adaptive hybridized discontinuous Galerkin method

Journal Article Computers and Fluids · October 30, 2025 Metric-based anisotropic mesh adaptation has proven effective for the solution of both steady and unsteady problems in terms of reduced computational time and accuracy gain. Especially for time-dependent problems, its generalization to implicit high-order ... Full text Cite

Conservative solution transfer between anisotropic meshes for time-accurate hybridized discontinuous Galerkin methods

Journal Article International Journal for Numerical Methods in Fluids · June 1, 2024 We present a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. In particular, we focus on a coupling of the solution process for unsteady problems with our anisotropic mesh refinement framework. The goal is to properly ... Full text Cite

Adjoint-based aerodynamic shape optimization with hybridized discontinuous Galerkin methods

Journal Article Computers and Fluids · January 15, 2024 We present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for gene ... Full text Cite

A Hybridized Discontinuous Galerkin Finite Element Method for Multi-Physics Problems

Conference AIAA Scitech Forum and Exposition 2024 · January 1, 2024 This paper presents one of the first high-order simulations of inductively coupled plasma (ICP). First, a multi-domain solver using a variant of discontinuous Galerkin method, called the hybridized discontinuous Galerkin method, is developed. This multi-do ... Full text Cite

Prediction of a Laminar Separation Bubble on low-Reynolds Airfoils using Variational Multiscale Method

Conference AIAA Aviation Forum and Ascend 2024 · January 1, 2024 The paper presents the application of a finite element numerical approach for predicting the development and locating the Laminar Separation Bubble (LSB) on low Reynolds airfoils. The method is a linearized and segregated variation of the Variational Multi ... Cite

PASSIVE FLOW CONTROL DEVICES ON LOW-REYNOLDS DU89-134 AIRFOIL

Conference Icas Proceedings · January 1, 2024 Passive Flow Control abstract. ... Cite

Metric-based anisotropic mesh adaptation for viscoelastic flows

Journal Article Computers and Mathematics with Applications · December 1, 2023 The computation of flows of viscoelastic fluids is expensive compared to standard fluids. Besides degrees-of-freedom for velocity and pressure, the viscoelastic stresses introduce an additional unknown to the system. While adaptive meshing techniques are c ... Full text Cite

A continuous hp-mesh model for discontinuous Petrov-Galerkin finite element schemes with optimal test functions

Journal Article Computers and Mathematics with Applications · October 1, 2023 We present an anisotropic hp-mesh adaptation strategy using a continuous mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with optimal test functions, extending our previous work [1] on h-adaptation. The proposed strategy utilizes ... Full text Cite

An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control

Journal Article Journal of Scientific Computing · May 1, 2023 We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed space-time cylinder Ω× (0 , T). We employ the space-time discontinuous Galerkin method which enables us to use ... Full text Cite

Conservative Solution Transfer Between Anisotropic Meshes for Adaptive Time-Accurate Hybridized Discontinuous Galerkin Methods

Conference AIAA Scitech Forum and Exposition 2023 · January 1, 2023 We present a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. We focus in particular on a coupling of the solution process for unsteady problems with an anisotropic mesh refinement framework. The goal is to properly r ... Full text Cite

Aerodynamic Shape Optimization with Hybridized Discontinuous Galerkin Schemes

Conference AIAA Scitech Forum and Exposition 2023 · January 1, 2023 We present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for gene ... Full text Cite

A review and comparison of error estimators for anisotropic mesh adaptation for flow simulations

Journal Article Computers and Fluids · February 15, 2022 Automated mesh adaptation is known to be an efficient way to control discretization errors in Computational Fluid Dynamics (CFD) simulations. It offers the added advantage that the user only needs to have a minimal expertise in generating appropriate meshe ... Full text Cite

An anisotropic h-adaptive strategy for discontinuous Petrov-Galerkin schemes using a continuous mesh model

Journal Article Computers and Mathematics with Applications · January 15, 2022 Certain Petrov-Galerkin schemes deliver inherently stable formulations of variational problems on a given mesh by selecting appropriate pairs of trial and test spaces. These schemes are especially suited for adaptation, due to their inherent ability to yie ... Full text Cite

Introduction

Chapter · January 1, 2022 The goal of the first chapter is to present a brief motivation for the anisotropic mesh adaptation method and to illustrate its potential. We start the exposition by recalling several well-known facts concerning the numerical analysis of Galerkin (or finit ... Full text Cite

Anisotropic Mesh Adaptation Method, hp-Variant

Chapter · January 1, 2022 We present an hp-variant of the anisotropic mesh adaptation methods discussed so far. That is, contrary to our discussion in Chap. 5, we now let the polynomial degree of approximation vary from mesh element to mesh element. This is essential in situations ... Full text Cite

Goal-Oriented Anisotropic Mesh Adaptation

Chapter · January 1, 2022 Employing the results from the previous chapter, we derive goal-oriented error estimates including the geometry of mesh elements. These estimates are based on interpolation error bounds. Furthermore, we present a goal-oriented anisotropic hp-mesh adaptatio ... Full text Cite

Implementation Aspects

Chapter · January 1, 2022 We present some implementation aspects of the anisotropic hp-mesh adaptation algorithms. In particular, in Sect. 9.1, we present higher-order reconstruction techniques which are required by our algorithms for estimating of the interpolation error. Moreover ... Full text Cite

Applications

Chapter · January 1, 2022 We present several additional applications of the anisotropic hp-mesh adaptation methods to more practical problems. In particular, we deal with compressible flow acting on an isolated profile, time-dependent viscous shock-vortex interaction, and porous me ... Full text Cite

Interpolation Error Estimates for Two Dimensions

Chapter · January 1, 2022 We formulate the fundamental theoretical results which are later employed for the anisotropic mesh adaptation method. First, we recall the geometry terms of a mesh triangle K discussed in the previous chapter. Further, we define an interpolation of a suffi ... Full text Cite

Anisotropic Mesh Adaptation Method, h-Variant

Chapter · January 1, 2022 We discuss the construction of optimal meshes with respect to the interpolation error introduced in Chaps. 3 and 4. In particular, the goal is to construct a simplicial mesh such that the corresponding interpolation error is minimal, while the number of de ... Full text Cite

Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods

Journal Article Applied and Computational Mechanics · January 1, 2022 The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely ba ... Full text Cite

Framework of the Goal-Oriented Error Estimates

Chapter · January 1, 2022 In many practical applications, we are not interested in the solution u of the given partial differential equations as such, but in the value of a certain quantity of interest, which depends on the solution. ... Full text Cite

Interpolation Error Estimates for Three Dimensions

Chapter · January 1, 2022 We extend the theoretical results to the three-dimensional case. In the same spirit as for the two-dimensional case, we recall the geometry of a tetrahedron K and define the interpolation error function and the corresponding error estimates. The extension ... Full text Cite

Metric Based Mesh Representation

Chapter · January 1, 2022 In this chapter, we formulate the initial problems related to the partition of the given domain Ω into a simplicial mesh. Furthermore, we recall the concept of the representation of simplicial meshes by a metric field, which is at the core of anisotropic m ... Full text Cite

A hybridized discontinuous galerkin solver for high-speed compressible flow

Journal Article Aerospace · November 1, 2021 We present a high-order consistent compressible flow solver, based on a hybridized discontinuous Galerkin (HDG) discretization, for applications covering subsonic to hypersonic flow. In the context of high-order discretization, this broad range of applicat ... Full text Cite

A residual-based hp-mesh optimization technique for petrov-galerkin schemes with optimal test functions.

Conference World Congress in Computational Mechanics and Eccomas Congress · January 1, 2021 In recent times, Petrov-Galerkin schemes with optimal test function framework have presented themselves as a stable and robust technique for solving partial differential equations. These schemes are also accompanied by an inbuilt error estimator, which mak ... Full text Cite

Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model

Journal Article Journal of Computational Physics · May 15, 2020 In this paper we propose an adjoint-based hp-adaptation method for conservation laws, and corresponding numerical schemes based on piecewise polynomial approximation spaces. The method uses a continuous mesh framework, similar to that proposed in [1], wher ... Full text Cite

A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems

Journal Article Computers and Mathematics with Applications · November 1, 2019 We deal with the numerical solution of linear convection–diffusion–reaction equations using the hp-variant of the discontinuous Galerkin method on triangular grids. We develop a mesh adaptive algorithm which modifies the size and shape of mesh elements and ... Full text Cite

Metric construction for error control of finite element solutions

Conference AIAA Aviation 2019 Forum · January 1, 2019 We have previously presented error models for finite-element methods (FEM), which can be used to drive metric-based anisotropic adaptation in a parameter free way. While numerical results were presented using primarily our in-house hybridized Discontinuous ... Full text Cite

A goal-oriented high-order anisotropic mesh adaptation using discontinuous Galerkin method for linear convection-diffusion-reaction problems

Journal Article SIAM Journal on Scientific Computing · January 1, 2019 We deal with the numerical solution of a linear convection-diffusion-reaction equation using the discontinuous Galerkin method of arbitrary polynomial approximation degree on anisotropic triangular grids. We derive a posteriori goal-oriented error estimate ... Full text Cite

A goal oriented optimization technique for tetrahedral grids using a continuous-mesh model

Conference AIAA Scitech 2019 Forum · January 1, 2019 We have previously proposed a metric-based anisotropic adaption method for tetrahedral grids. In the present paper, we extend our method to goal oriented adaptation. Target-based adaptation is realized using a suitable adjoint-based error estimate for thre ... Full text Cite

A continuous hp-mesh model for adaptive discontinuous Galerkin schemes

Journal Article Applied Numerical Mathematics · February 1, 2018 We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method wh ... Full text Cite

Class of space-time entropy stable dg schemes for systems of convection–diffusion

Conference Springer Proceedings in Mathematics and Statistics · January 1, 2018 In this work, we present a family of entropy stable discontinuous Galerkin methods for systems of convection–diffusion with nonlinear convective and viscous fluxes. The discretization presented here is based on a mixed formulation and is designed to preser ... Full text Cite

Mesh optimization for discontinuous galerkin methods using a continuous mesh model

Journal Article AIAA Journal · January 1, 2018 A method for anisotropic mesh adaptation and optimization for high-order discontinuous Galerkin schemes is presented. Given the total number of degrees of freedom, a metric-based method is proposed, which aims to globally optimize the mesh with respect to ... Full text Cite

A continuous-mesh optimization technique for piecewise polynomial approximation on tetrahedral grids

Conference 2018 Fluid Dynamics Conference · January 1, 2018 Building on previous research we presenl a three-dimensional formulation of a metric-based mesh optimization scheme. The intended application area is higher order (discontinuous) Galcrkin schemes for convectioii-dilfusion problems. Ultimately, as in our pr ... Full text Cite

Anisotropic hp-mesh optimization technique based on the continuous mesh and error models

Journal Article Computers and Mathematics with Applications · July 1, 2017 We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the hp-version of the finite element method (hp-FEM). The technique uses a combination of approximation and interpolation error estimates to ... Full text Cite

Entropy stable discontinuous galerkin scheme for the compressible Navier-stokes equations

Conference AIAA Scitech Forum 55th AIAA Aerospace Sciences Meeting · January 1, 2017 In this paper, we present a family of entropy-stable discontinuous Galerkin methods for the compressible Navier-Stokes equations. The discretization presented here is based on a mixed formulation, and is designed to preserve the entropy stability of an alr ... Full text Cite

Adjoint-based anisotropic mesh adaptation for discontinuous Galerkin methods using a continuous mesh model

Conference 23rd AIAA Computational Fluid Dynamics Conference 2017 · January 1, 2017 In this paper we propose an adjoint-based mesh optimization method for conservation laws, which may be used with any numerical method based on piecewise polynomials. The method uses a continuous mesh framework, similar to that proposed in [19], where a glo ... Full text Cite

Adjoint-based hp-adaptivity on anisotropic meshes for high-order compressible flow simulations

Journal Article Computers and Fluids · November 5, 2016 We present an efficient adjoint-based hp-adaptation methodology on anisotropic meshes for high order Discontinuous Galerkin schemes applied to (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations. The refi ... Full text Cite

On the convergence of a shock capturing discontinuous galerkin method for nonlinear hyperbolic systems of conservation laws

Journal Article SIAM Journal on Numerical Analysis · January 1, 2016 In this paper, we present a shock capturing discontinuous Galerkin method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time formulation in terms of entro ... Full text Cite

High order entropy stable discontinuous Galerkin schemes in a space-time computational framework

Conference 46th AIAA Fluid Dynamics Conference · January 1, 2016 In this paper we present a space-time computational framework for solution of nonlinear hyperbolic systems of conservation laws. The framework is based on a previously proposed space-time discontinuous Galerkin discretization, realized in terms of entropy ... Full text Cite

On the convergence of space-time discontinuous Galerkin schemes for scalar conservation laws?

Journal Article SIAM Journal on Numerical Analysis · January 1, 2016 We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone flux functions ... Full text Cite

Mesh adaptation and optimization for discontinuous galerkin methods using a continuous mesh model

Conference 2016 AIAA Modeling and Simulation Technologies Conference · January 1, 2016 We present a method for anisotropic mesh adaptation and optimization for high-order Discontinuous Galerkin (DG) Schemes. Given the total number of degrees of freedom, we propose a metric-based method, which aims to globally optimize the mesh with respect t ... Full text Cite

An anisotropic adjoint-based hp-adaptive HDG method for compressible turbulent flow

Conference 53rd AIAA Aerospace Sciences Meeting · January 1, 2015 We present an anisotropic adjoint-based hp-adaptive hybridized discontinuous Galerkin method for turbulent compressible ow. We use the Reynolds-averaged Navier-Stokes equations complemented with the k-ω turbulence model. By means of hybridization, we can f ... Full text Cite

A unifying computational framework for adaptive high-order finite element methods

Conference 22nd AIAA Computational Fluid Dynamics Conference · January 1, 2015 We present a comprehensive overview of our computational framework for adaptive high-order finite element methods, including discontinuous Galerkin (DG) methods and their hybridized counterparts (HDG). Besides covering the numerical methods, we grant their ... Full text Cite

Hp-adaptivity on anisotropic meshes for hybridized discontinuous Galerkin scheme

Conference 22nd AIAA Computational Fluid Dynamics Conference · January 1, 2015 We present an efficient adaptation methodology on anisotropic meshes for the recently developed hybridized discontinuous Galerkin scheme for (nonlinear) convection-diffusion problems, including compressible Euler and Navier-Stokes equations. The methodolog ... Full text Cite

A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows

Journal Article Journal of Scientific Computing · January 1, 2015 Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for compressible fluid flow. The extension of the multiresolution-based mesh adaptation concept to high-order discontinuous Galerkin disc ... Full text Cite

Adjoint-based error estimation and mesh adaptation for hybridized discontinuous Galerkin methods

Journal Article International Journal for Numerical Methods in Fluids · December 20, 2014 We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations. The hybridization ... Full text Cite

A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow

Journal Article Computers and Fluids · July 2, 2014 Objective: We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation for compressible flow problems. The aim is to provide a critical assessment of the computational efficiency ... Full text Cite

An adjoint consistency analysis for a class of hybrid mixed methods

Journal Article IMA Journal of Numerical Analysis · January 1, 2014 Hybrid methods represent a classic discretization paradigm for elliptic equations. More recently, hybrid methods have been formulated for convection-diffusion problems, in particular compressible fluid flow. In Schütz and May (2013, AICES Technical Report ... Full text Cite

A hybridized discontinuous Galerkin method for turbulent compressible flow

Conference 44th AIAA Fluid Dynamics Conference · January 1, 2014 We present a hybridized discontinous Galerkin method for two-dimensional turbulent compressible flow. More precisely, we use the Reynolds-averaged Navier-Stokes equations complemented with the k-ω turbulence model devised by Wilcox [21] and modified by Bas ... Full text Cite

A hybridized discontinuous Galerkin method for three-dimensional compressible flow problems

Conference 52nd Aerospace Sciences Meeting · January 1, 2014 We present a hybridized discontinuous Galerkin method for three-dimensional flow problems. As an implementation technique hybridization is a classic paradigm for dual-mixed finite element discretizations. Hybridization of finite element discretizations has ... Cite

A hybridized discontinuous galerkin method for three-dimensional compressible flow problems

Conference 52nd AIAA Aerospace Sciences Meeting AIAA Science and Technology Forum and Exposition Scitech 2014 · January 1, 2014 We present a hybridized discontinuous Galerkin method for three-dimensional ow problems. As an implementation technique hybridization is a classic paradigm for dual-mixed finite element discretizations. Hybridization of finite element discretizations has t ... Full text Cite

High-order CFD methods: Current status and perspective

Journal Article International Journal for Numerical Methods in Fluids · July 20, 2013 After several years of planning, the 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7-8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astron ... Full text Cite

A hybrid mixed method for the compressible Navier-Stokes equations

Journal Article Journal of Computational Physics · May 1, 2013 We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a Mixed me ... Full text Cite

A note on adjoint error estimation for one-dimensional stationary balance laws with shocks

Journal Article SIAM Journal on Numerical Analysis · April 17, 2013 We consider one-dimensional steady-state balance laws with discontinuous solutions. Giles and Pierce [J. Fluid Mech., 426 (2001), pp. 327-345] realized that a shock leads to a new term in the adjoint error representation for target functionals. This term d ... Full text Cite

Adjoint-based hp-adaptation for a class of high-order hybridized finite element schemes for compressible flows

Conference 21st AIAA Computational Fluid Dynamics Conference · January 1, 2013 We present a robust and effcient hp-adaptation methodology, building on a class of hybridized finite element schemes for (nonlinear) convection-diffusion problems, including compressible Euler and Navier-Stokes equations. Using a discrete-adjoint approach, ... Full text Cite

A hybridized DG/mixed scheme for nonlinear advection-diffusion systems, including the compressible Navier-Stokes equations

Conference 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition · December 1, 2012 We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a mixed me ... Full text Cite

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Journal Article Journal of Computational Physics · March 1, 2012 Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Di ... Full text Cite

Time-relaxation methods for high-order discretization of compressible flow problems

Conference Aip Conference Proceedings · November 28, 2011 We present recent developments in solution methods for steady compressible flow simulation in conjunction with high-order spatial discretization methods. Lack of efficient solution methods has often been identified as a major deficiency of high-order techn ... Full text Cite

On the connection between the spectral difference method and the discontinuous Galerkin method

Journal Article Communications in Computational Physics · January 1, 2011 In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin (DG) discretization of a nonlinear conservation law. This allows interpretation of the Spectral Difference Scheme as a particular discretization unde ... Full text Cite

Efficient relaxation methods for high-order discretization of steady problems

Chapter · January 1, 2011 We review the current status of solution methods for nonlinear systems arising from high-order discretization of steady compressible flow problems. In this context, many of the difficulties that one faces are similar to, but more pronounced than, those tha ... Cite

Analytical and numerical investigation of the influence of artificial viscosity in discontinuous galerkin methods on an adjoint-based error estimator

Conference Computational Fluid Dynamics 2010 Proceedings of the 6th International Conference on Computational Fluid Dynamics Iccfd 2010 · January 1, 2011 Recently, it has been observed that the standard approximation to the dual solution in a scalar finite difference context can actually fail if the underlying forward solution is not smooth (Giles and Ulbrich, Convergence of linearised and adjoint approxima ... Full text Cite

An adaptive multiwavelet-based DG discretization for compressible fluid flow

Conference Computational Fluid Dynamics 2010 Proceedings of the 6th International Conference on Computational Fluid Dynamics Iccfd 2010 · January 1, 2011 Adaptation methods based on multiresolution analysis using biorthogonal wavelets have been successfully used with Finite-Volume solvers for compressible fluid flow. The extension of the concept to higher-order Discontinuous Galerkin (DG) discretization may ... Full text Cite

A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

Journal Article Journal of Computational Physics · April 20, 2010 Higher order discretization has not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably to ... Full text Cite

Relaxation techniques for high-order discretizations of steady compressible inviscid flows

Conference 40th AIAA Fluid Dynamics Conference · January 1, 2010 There does not exist a definite best strategy to advance high-order discretizations of inviscid compressible flows to steady state. The need for a wide range of possible time-relaxation strategies is determined by different possible difficulties: stability ... Full text Cite

Effcient algorithms for high-order discretizations of the Euler and Navier-Stokes equations

Conference 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition · December 1, 2009 Higher order discretizations have not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably ... Cite

Convergence acceleration for simulation of steady-state compressible flows using high-order schemes

Conference 19th AIAA Computational Fluid Dynamics Conference · January 1, 2009 The formulation of strategies for high-order discretization methods for compressible flow simulations is now to a certain extent understood, whereas the development of techniques for efficiently solving the resulting discrete equations has generally been l ... Full text Cite

Spectral difference method for unstructured grids II: Extension to the Euler equations

Journal Article Journal of Scientific Computing · July 1, 2007 An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve high-computatio ... Full text Cite

An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow

Journal Article Journal of Computational Physics · January 10, 2007 During the past decade gas-kinetic methods based on the BGK simplification of the Boltzmann equation have been employed to compute fluid flow in a finite-difference or finite-volume context. Among the most successful formulations is the finite-volume schem ... Full text Cite

A spectral difference method for the euler and navier-stokes equations on unstructured meshes

Conference Collection of Technical Papers 44th AIAA Aerospace Sciences Meeting · January 1, 2006 This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for sc ... Full text Cite

Unstructured algorithms for inviscid and viscous flows embedded in a unified solver architecture: Flo3xx

Conference 43rd AIAA Aerospace Sciences Meeting and Exhibit Meeting Papers · December 1, 2005 This paper reports recent progress towards a new platform for computational aero-dynamics on arbitrary meshes, tentatively designated Flo3xx. This tool is designed for maximum flixibility to serve as both an industrial strength flow solver on general grids ... Cite

Calculating three-dimensional transonic flow using a gas-kinetic BGK finite-volume method

Conference 43rd AIAA Aerospace Sciences Meeting and Exhibit Meeting Papers · December 1, 2005 The BGK method has been previously used to compute two-dimensional viscous flow and inviscid flow. In this paper we will build on the theoretical framework of the BGK method to develop a scheme for arbitrary meshes, as well as show two- and three-dimension ... Cite

High-order accurate methods for high-speed flow

Conference 17th AIAA Computational Fluid Dynamics Conference · January 1, 2005 This work focuses on high-order numerical schemes for conservation laws with emphasis on problems that admit discontinuous solutions. We will investigate several enabling techniques with the aim to construct robust methods for unstructured meshes capable o ... Full text Cite

Improved gaskinetic multigrid method for three-dimensional computation of viscous flow

Conference 17th AIAA Computational Fluid Dynamics Conference · January 1, 2005 In this paper we build on the framework of the gas-kinetic BGK method with the aim to develop an industrial strength flow solver on arbitrary meshes. To that end we present a modified, more efficient formulation of the BGK scheme, to reduce the extreme cos ... Full text Cite

Drag prediction of the DLR-F6 configuration

Conference AIAA Paper · July 1, 2004 Out of a host of experimental aerodynamic data available for the DLR-F6 configuration a set of reference test cases has been chosen for the second AIAA drag prediction workshop. Participants of the workshop were invited to use state-of-the-art tools for co ... Cite