3 citations · 4 across the 6 of their papers we have counts for
6 papers
Numerical boundary flux functions that give provable bounds for nonlinear initial boundary value problems with open boundaries
Andrew R. Winters, David A. Kopriva, Jan Nordström
We present a strategy for interpreting nonlinear, characteristic-type penalty terms as numerical boundary flux functions that provide provable bounds for solutions to nonlinear hyp…
Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry
David A. Kopriva, Andrew R. Winters, Jan Nordström
Meshes approximate the boundaries of a geometry when the boundaries are curved. The accuracy of the mesh then affects the error of computations of initial boundary value problems f…
Mimetic Metrics for the DGSEM
Daniel Bach, Andrés Rueda-Ramírez, David A. Kopriva +1
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 discr…
Energy Bounds for Discontinuous Galerkin Spectral Element Approximations of Well-Posed Overset Grid Problems for Hyperbolic Systems
David A. Kopriva, Andrew R. Winters, Jan Nordström
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 app…
Analysis of an Explicit, High-Order Semi-Lagrangian Nodal Method
Gustaaf B. Jacobs, Hareshram Natarajan, Pavel Popov +1
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 interp…
On the Theoretical Foundation of Overset Grid Methods for Hyperbolic Problems II: Entropy Bounded Formulations for Nonlinear Conservation Laws
David A. Kopriva, Gregor J. Gassner, Jan Nordstrom
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximat…