5 papers · 1 filter
Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction
Jesse CHan, Hendrik Ranocha, Raymond Park +3
Structure-preserving discontinuous Galerkin (DG) methods typically improve the robustness of high order simulations of real fluids. In addition to conservation, key structures incl…
Why summation by parts is not enough
Jan Glaubitz, Armin Iske, Joshua Lampert +1
We investigate the construction and performance of summation-by-parts (SBP) operators, which offer a powerful framework for the systematic development of structure-preserving numer…
Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators
Jan Glaubitz, Joshua Lampert, Andrew R. Winters +1
Overset grid methods handle complex geometries by overlapping simpler, geometry-fitted grids to cover the original, more complex domain. However, ensuring their stability---particu…
Structure-Preserving Numerical Methods for Fokker-Planck Equations
Hanna Bartel, Joshua Lampert, Hendrik Ranocha
A common way to numerically solve Fokker-Planck equations is the Chang-Cooper method in space combined with one of the Euler methods in time. However, the explicit Euler method is…
Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
Joshua Lampert, Hendrik Ranocha
We use the general framework of summation-by-parts operators to construct conservative, energy-stable, and well-balanced semidiscretizations of two different nonlinear systems of d…