134 citations · 1.1k across the 79 of their papers we have counts for
12 papers · 1 filter
Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations
Hendrik Ranocha, David I. Ketcheson
We propose and study a class of arbitrarily high-order numerical discretizations that preserve multiple invariants and are essentially explicit (they do not require the solution of…
Compact Runge-Kutta flux reconstruction methods for non-conservative hyperbolic equations
Arpit Babbar, Hendrik Ranocha
Compact Runge-Kutta (cRK) Flux Reconstruction (FR) methods are a variant of RKFR methods for hyperbolic conservation laws with a compact stencil including only immediate neighborin…
Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
Sebastian Bleecke, Abhijit Biswas, David I. Ketcheson +2
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods…
High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization
Hendrik Ranocha, David I. Ketcheson
We propose a class of numerical methods for the nonlinear Schrödinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and re…
Structure-Preserving High-Order Methods for the Compressible Euler Equations in Potential Temperature Formulation for Atmospheric Flows
Marco Artiano, Oswald Knoth, Peter Spichtinger +1
We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxe…
Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
Ferdinand Thein, Hendrik Ranocha
The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressu…
The domain-of-dependence stabilization for cut-cell meshes is fully discretely stable
Louis Petri, Gunnar Birke, Christian Engwer +1
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by red…
Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions
Jan Giesselmann, Hendrik Ranocha
We prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin-Bona-Mahony, Korteweg-de Vries, Gardner, Kawahara, and Kuramo…
Real-time rail vehicle localisation using spatially resolved magnetic field measurements
Niklas Dieckow, Katharina Ostaszewski, Philip Heinisch +2
This work presents two complementary real-time rail vehicle localization methods based on magnetic field measurements and a pre-recorded magnetic map. The first uses a particle fil…
Paired Explicit Relaxation Runge-Kutta Methods: Entropy-Conservative and Entropy-Stable High-Order Optimized Multirate Time Integration
Daniel Doehring, Hendrik Ranocha, Manuel Torrilhon
We present novel entropy-conservative and entropy-stable multirate Runge-Kutta methods based on Paired Explicit Runge-Kutta (P-ERK) schemes with relaxation for conservation laws an…
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner +3
The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values as independent degrees of freedom, based on ideas from fini…
Automatic differentiation for performing the Cauchy-Kovalevskaya procedure in Lax-Wendroff type discretizations
Arpit Babbar, Valentin Churavy, Michael Schlottke-Lakemper +1
Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbol…