134 citations · 1.1k across the 79 of their papers we have counts for
11 papers · 1 filter
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
Hendrik Ranocha, Gregor J Gassner
Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the sim…
A conservative fully-discrete numerical method for the regularised shallow water wave equations
Dimitrios Mitsotakis, Hendrik Ranocha, David I. Ketcheson +1
The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and…
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha +1
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravit…
Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts
Philippe G. LeFloch, Hendrik Ranocha
We study nonlinear hyperbolic conservation laws with non-convex flux in one space dimension and, for a broad class of numerical methods based on summation by parts operators, we co…
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
Hendrik Ranocha, Dimitrios Mitsotakis, David I. Ketcheson
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta met…
Positivity-Preserving Adaptive Runge-Kutta Methods
Stephan Nüßlein, Hendrik Ranocha, David I Ketcheson
Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the model is solved…
Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL
Philip Heinisch, Katharina Ostaszewski, Hendrik Ranocha
When considering different hardware platforms, not just the time-to-solution can be of importance but also the energy necessary to reach it. This is not only the case with battery…
Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
Hendrik Ranocha, Lisandro Dalcin, Matteo Parsani
Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generali…
A New Class of Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions
Hendrik Ranocha, Jan Nordström
Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP)…
General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
Hendrik Ranocha, Lajos Lóczi, David I. Ketcheson
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-K…
Relaxation Runge-Kutta Methods for Hamiltonian Problems
Hendrik Ranocha, David I. Ketcheson
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior o…