7 papers
A well posed and stable canonical evaporation model problem for phase-change in two-phase flows
Jan Nordström
We formulate a well posed interface formulation for canonical one-dimensional evaporation two-phase model problems (the Stefan and Sucking problems) commonly used to validate produ…
Summation-by-parts operators for general function spaces: optimal nodes
Nicholas Hale, Charis Harley, Prince Nchupang +1
Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed…
From Exact Space-Time Symmetry Conservation to Automatic Mesh Refinement in Discrete Initial Boundary Value Problems
Alexander Rothkopf, W. A. Horowitz, Jan Nordström
In this contribution we present recent developments in the formulation and solution of Initial Boundary Value Problems (IBVPs). Building upon a modern variational action formulatio…
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…
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 -- partic…
Linear and Nonlinear Boundary Conditions: What's the difference?
Jan Nordström
In previous work, we derived new energy and entropy stable open boundary conditions and implementation procedures for linear and nonlinear initial boundary value problems. These bo…