134 citations · 1.1k across the 79 of their papers we have counts for
84 papers
GPU-Accelerated Nested Schur-Complement Solvers for Atmospheric Flow Simulations Using Horizontally-Explicit, Vertically-Implicit Schemes and Discontinuous Galerkin Methods
Marco Artiano, Andrés Rueda-Ramírez, Oswald Knoth +2
Horizontally explicit, vertically implicit (HEVI) time integration removes the acoustic time-step restriction imposed by fine vertical grids in nonhydrostatic atmospheric models, b…
Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form
Marco Artiano, Kieran Ricardo, Oswald Knoth +2
We develop structure-preserving methods for the compressible Euler equations with gravity in vector-invariant form and potential temperature as a prognostic variable within the flu…
Perspectives on Sustainable Computational Science and Engineering
Julia Kowalski, Ann S. Almgren, Achim Basermann +43
Computational Science and Engineering (CSE) combines expertise at the intersection of engineering, applied mathematics, and computer science to form powerful methods for model-base…
Nodal discontinuous Galerkin methods for non-ideal equations of state: pressure equilibrium preservation and entropy correction
Jesse CHan, Hendrik Ranocha, Raymond Park +3
Structure-preserving discontinuous Galerkin (DG) methods typically improve the robustness of high order simulations of real fluids. In addition to conservation, key structures incl…
Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws
Hendrik Ranocha
Although entropy-based summation-by-parts (SBP) discretizations of hyperbolic conservation laws are widely used for their robustness and stability properties, there are very few re…
Multi-Solver Coupling for Parallel Adaptive Multi-Physics Simulations with Trixijl and dealII
Vivienne Ehlert, Gregor Gassner, Martin Kronbichler +2
Many standalone frameworks for numerical solvers have been developed to tackle the simulation of specific single- or multi-physics problems. For solving coupled problems, common ap…
Massively parallel numerical simulations with Julia
Simon Candelaresi, Benedict Geihe, Marco Artiano +6
The Julia programming language aims to provide a modern approach to develop high-performance computing (HPC) applications. It tries to achieve this by combining a high-level, dynam…
Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
Jan Giesselmann, Fabio Leotta, Hendrik Ranocha +1
We study a hyperbolic approximation ("hyperbolization") of the Cahn-Hilliard (CH) equation, originally proposed by Dhaouadi, Dumbser, and Gavrilyuk (2025, DOI: 10.1098/rspa.2024.06…
Asymptotic-Preserving and Well-Balanced Linearly Implicit IMEX Schemes for the Anelastic Limit of the Isentropic Euler Equations with Gravity
Marco Artiano, Hendrik Ranocha, Saurav Samantaray
We consider the compressible Euler system with anelastic scaling, modeling isentropic flows under the influence of gravity. In the zero-Mach-number limit, the solution of the compr…
A Positivity-Preserving Relaxation Algorithm
Thomas Izgin, Hendrik Ranocha, Chi-Wang Shu
We combine Patankar-type methods with suitable relaxation procedures that are capable of ensuring correct dissipation or conservation of functionals such as entropy or energy while…
Compact Runge-Kutta flux reconstruction methods with entropy and/or kinetic energy preserving fluxes
Arpit Babbar, Qifan Chen, Hendrik Ranocha
Compact Runge-Kutta (cRK) methods are a class of high order methods for solving hyperbolic conservation laws characterized by their compact stencil including only immediate neighbo…
Volume Term Adaptivity for Discontinuous Galerkin Schemes
Daniel Doehring, Jesse Chan, Hendrik Ranocha +3
We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we…
On Affordable High-Order Entropy-Conservative/Stable and Well-Balanced Methods for Nonconservative Hyperbolic Systems
Marco Artiano, Hendrik Ranocha
Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving nu…
Jin-Xin relaxation as a shock-capturing method for high-order DG/FR schemes
Marco Artiano, Arpit Babbar, Michael Schlottke-Lakemper +2
Jin-Xin relaxation is a method for approximating non-linear hyperbolic conservation laws by a linear system of hyperbolic equations with an dependent stiff source ter…
An Energy-Preserving Domain of Dependence Stabilization for the Linear Wave Equation on Cut-Cell Meshes
Gunnar Birke, Christian Engwer, Sandra May +2
We present an energy-preserving (either energy-conservative or energy-dissipative) domain of dependence stabilization method for the linear wave equation on cut-cell meshes. Our sc…
Domain-of-dependence-stabilized cut-cell discretizations of linear kinetic models with summation-by-parts properties
Louis Petri, Sigrun Ortleb, Gunnar Birke +2
We employ the summation-by-parts (SBP) framework to extend the recent domain-of-dependence (DoD) stabilization for cut cells to linear kinetic models in diffusion scaling. Numerica…
GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations
Collin Wittenstein, Vincent Marks, Mario Ricchiuto +1
We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry and either periodic or re…
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…