167 citations · 598 across the 41 of their papers we have counts for
42 papers
High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations
Jesse Chan, Khemraj Shukla, Xinhui Wu +2
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes add…
High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting
Yimin Lin, Jesse Chan
Subcell limiting strategies for discontinuous Galerkin spectral element methods do not provably satisfy a semi-discrete cell entropy inequality. In this work, we introduce an exten…
High-Order Methods for Hypersonic Flows with Strong Shocks and Real Chemistry
Ahmad Peyvan, Khemraj Shukla, Jesse Chan +1
We compare high-order methods including spectral difference (SD), flux reconstruction (FR), the entropy-stable discontinuous Galerkin spectral element method (ES-DGSEM), modal disc…
On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows
Jesse Chan, Hendrik Ranocha, Andres Rueda-Ramirez +2
High order entropy stable schemes provide improved robustness for computational simulations of fluid flows. However, additional stabilization and positivity preserving limiting can…
Entropy-Stable Gauss Collocation Methods for Ideal Magneto-Hydrodynamics
Andrés M Rueda-Ramírez, Florian J Hindenlang, Jesse Chan +1
In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto-hydrod…
A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
Yimin Lin, Jesse Chan, Ignacio Tomas
High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guara…
Entropy stable discontinuous Galerkin methods for the shallow water equations with subcell positivity preservation
Xinhui Wu, Nathaniel Trask, Jesse Chan
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features, and have traditionally required additional filtering, limi…
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
Hendrik Ranocha, Michael Schlottke-Lakemper, Jesse Chan +4
Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entro…
Provably Stable Flux Reconstruction High-Order Methods on Curvilinear Elements
Alexander Cicchino, David C. Del Rey Fernández, Siva Nadarajah +2
Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction (ES…
Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
Hendrik Ranocha, Michael Schlottke-Lakemper, Andrew R. Winters +3
We present Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi.jl is extensible…
Discrete adjoint computations for relaxation Runge-Kutta methods
Mario J. Bencomo, Jesse Chan
Relaxation Runge-Kutta methods reproduce a fully discrete dissipation (or conservation) of entropy for entropy stable semi-discretizations of nonlinear conservation laws. In this p…
Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations
Jesse Chan, Yimin Lin, Tim Warburton
Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. In this work, we…
A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation
Khemraj Shukla, Jesse Chan, Maarten V. de Hoop
Wave propagation in real media is affected by various non-trivial physical phenomena, e.g., anisotropy, an-elasticity and dissipation. Assumptions on the stress-strain relationship…
Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains
Xinhui Wu, Jesse Chan
We present a high-order entropy stable discontinuous Galerkin (ESDG) method for nonlinear conservation laws on both multi-dimensional domains and on networks constructed from one-d…
High order weight-adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes
Kaihang Guo, Jesse Chan
This paper presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed met…
Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes
Jesse Chan, Christina G. Taylor
Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to…
Mortar-based entropy-stable discontinuous Galerkin methods on non-conforming quadrilateral and hexahedral meshes
Jesse Chan, Mario J. Bencomo, David C. Del Rey Fernández
High-order entropy-stable discontinuous Galerkin (DG) methods for nonlinear conservation laws reproduce a discrete entropy inequality by combining entropy conservative finite volum…
High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration
Xinhui Wu, Jesse Chan, Ethan Kubatko
We present a high-order entropy stable discontinuous Galerkin (ESDG) method for the two dimensional shallow water equations (SWE) on curved triangular meshes. The presented scheme…
Entropy stable reduced order modeling of nonlinear conservation laws
Jesse Chan
Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-red…
A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities
Khemraj Shukla, Jesse Chan, Maarten V. de Hoop +1
We introduce a high-order weight-adjusted discontinuous Galerkin (WADG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in anisotropic porous…
A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media
Kaihang Guo, Sebastian Acosta, Jesse Chan
This paper presents a high-order discontinuous Galerkin (DG) scheme for the simulation of wave propagation through coupled elastic-acoustic media. We use a first-order stress-veloc…
Skew-symmetric entropy stable modal discontinuous Galerkin formulations
Jesse Chan
High order entropy stable discontinuous Galerkin (DG) methods for nonlinear conservation laws satisfy an inherent discrete entropy inequality. The construction of such schemes has…
Efficient entropy stable Gauss collocation methods
Jesse Chan, David C. Del Rey Fernandez, Mark H. Carpenter
The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and th…
Leapfrog time-stepping for Hermite methods
Arturo Vargas, Thomas Hagstrom, Jesse Chan +1
We introduce Hermite-leapfrog methods for first order wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors…