63 citations · 347 across the 39 of their papers we have counts for
6 papers · 1 filter
A Structured Approach to the Construction of Stable Linear Lattice-Boltzmann Collision Operators
Philipp Otte, Martin Frank
We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a wei…
Filtered Stochastic Galerkin Methods For Hyperbolic Equations
Jonas Kusch, Ryan G. McClarren, Martin Frank
Uncertainty Quantification for nonlinear hyperbolic problems becomes a challenging task in the vicinity of shocks. Standard intrusive methods lead to oscillatory solutions and can…
Ray Effect Mitigation for the Discrete Ordinates Method through Quadrature Rotation
Thomas Camminady, Martin Frank, Kerstin Küpper +1
Solving the radiation transport equation is a challenging task, due to the high dimensionality of the solution's phase space. The commonly used discrete ordinates (S) method su…
A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
M. Paul Laiu, Martin Frank, Cory D. Hauck
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scatter…
A short proof that sweeping is always possible for a spatial discretization with regular triangles and no hanging nodes
Thomas Camminady, Martin Frank
Sweeping is a commonly used procedure to explicitly solve the discrete ordinates equation, which itself is a common approximation of the neutron transport equation. To sweep throug…
A regularized entropy-based moment method for kinetic equations
Graham W. Alldredge, Martin Frank, Cory D. Hauck
We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the…