134 citations · 1.1k across the 79 of their papers we have counts for
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On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations
Diego Rojas, Radouan Boukharfane, Lisandro Dalcin +4
In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational a…
Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems
Hendrik Ranocha, David I. Ketcheson
Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the sam…
Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators
Hendrik Ranocha, Katharina Ostaszewski, Philip Heinisch
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimension…
Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization
Rémi Abgrall, Philipp Öffner, Hendrik Ranocha
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach…
Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
Hendrik Ranocha, Mohammed Sayyari, Lisandro Dalcin +2
The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Produc…
Some Notes on Summation by Parts Time Integration Methods
Hendrik Ranocha
Some properties of numerical time integration methods using summation by parts operators and simultaneous approximation terms are studied. These schemes can be interpreted as impli…