David A. Kopriva
YOU?
Author Swipe
View article: Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry
Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry Open
We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains ar…
View article: HOHQMesh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements
HOHQMesh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements Open
HOHQMesh generates unstructured all-quadrilateral and hexahedral meshes with high order boundaryinformation for use with spectral element solvers. Model input by the user requires only anoptional outer boundary curve plus any number of inn…
View article: Mimetic Metrics for the DGSEM
Mimetic Metrics for the DGSEM Open
Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discrete metric identities, i.e., have zero divergence. Divergen…
View article: Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems
Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems Open
We show that even though the Discontinuous Galerkin Spectral Element Method is stable for hyperbolic boundary-value problems, and the overset domain problem is well-posed in an appropriate norm, the energy of the approximation of the latte…
View article: : A high-order discontinuous Galerkin solver for flow simulations and multi-physics applications
: A high-order discontinuous Galerkin solver for flow simulations and multi-physics applications Open
We present the latest developments of our High-Order Spectral Element Solver ([Formula presented]), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows…
View article: p-Refinement with curvilinear elements for a discontinuous Galerkinspectral element method wave equation solver
p-Refinement with curvilinear elements for a discontinuous Galerkinspectral element method wave equation solver Open
There is a need to develop high order numerical methods to advance computational fluid dynamics, especially in the automotive, energy and aerospace fields. The discontinuous Galerkin spectral element method (DGSEM) provides higher accuracy…
View article: Analysis of an Explicit, High-Order Semi-Lagrangian Nodal Method
Analysis of an Explicit, High-Order Semi-Lagrangian Nodal Method Open
A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport equati…
View article: On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws Open
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving formulat…
View article: On the theoretical foundation of overset grid methods for hyperbolic problems: Well-posedness and conservation
On the theoretical foundation of overset grid methods for hyperbolic problems: Well-posedness and conservation Open
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space dime…
View article: On the Theoretical Foundation of Overset Grid Methods for Hyperbolic\n Problems: Well-Posedness and Conservation
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic\n Problems: Well-Posedness and Conservation Open
We use the energy method to study the well-posedness of initial-boundary\nvalue problems approximated by overset mesh methods in one and two space\ndimensions for linear constant-coefficient hyperbolic systems. We show that in\none space d…
View article: A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear\n Hyperbolic Systems
A Split-Form, Stable CG/DG-SEM for Wave Propagation Modeled by Linear\n Hyperbolic Systems Open
We present a hybrid continuous and discontinuous Galerkin spectral element\napproximation that leverages the advantages of each approach. The continuous\nGalerkin approximation is used on interior element faces where the equation\nproperti…
View article: Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations Open
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perf…
View article: Stability of Wall Boundary Condition Procedures for Discontinuous Galerkin Spectral Element Approximations of the Compressible Euler Equations
Stability of Wall Boundary Condition Procedures for Discontinuous Galerkin Spectral Element Approximations of the Compressible Euler Equations Open
We perform a linear and entropy stability analysis for wall boundary condition procedures for discontinuous Galerkin spectral element approximations of the compressible Euler equations. Two types of boundary procedures are examined. The fi…
View article: A Statically Condensed Discontinuous Galerkin Spectral Element Method on\n Gauss-Lobatto Nodes for the Compressible Navier-Stokes Equations
A Statically Condensed Discontinuous Galerkin Spectral Element Method on\n Gauss-Lobatto Nodes for the Compressible Navier-Stokes Equations Open
We present a static-condensation method for time-implicit discretizations of\nthe Discontinuous Galerkin Spectral Element Method on Gauss-Lobatto points\n(GL-DGSEM). We show that, when solving the compressible Navier-Stokes\nequations, it …
View article: Assessing Standard and Kinetic Energy Conserving Discontinuous Galerkin Formulations for Marginally Resolved Navier-Stokes Flows
Assessing Standard and Kinetic Energy Conserving Discontinuous Galerkin Formulations for Marginally Resolved Navier-Stokes Flows Open
The robustness and accuracy of marginally resolved discontinuous Galerkin spectral element computations are evaluated for the standard formulation and a kinetic energy conserving split form on complex flow problems of physical and engineer…
View article: Naturally curved quadrilateral mesh generation using an adaptive spectral element solver
Naturally curved quadrilateral mesh generation using an adaptive spectral element solver Open
We describe an adaptive version of a method for generating valid naturally curved quadrilateral meshes. The method uses a guiding field, derived from the concept of a cross field, to create block decompositions of multiply connected two di…