Efficient computation of Jacobian matrices for entropy stable summation-by-parts schemes
arXiv:2006.07504
Abstract
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 as flux differencing. We provide simple and efficient formulas for Jacobian matrices for the semi-discrete systems of ODEs produced by entropy stable discretizations. These formulas are derived based on the structure of flux differencing and derivatives of flux functions, which can be computed using automatic differentiation (AD). Numerical results demonstrate the efficiency and utility of these Jacobian formulas, which are then used in the context of two-derivative explicit time-stepping schemes and implicit time-stepping.
References in corpus (10)
- Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations
- Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations
- On discretely entropy conservative and entropy stable discontinuous Galerkin methods
- A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
- Forward-Mode Automatic Differentiation in Julia
- GPU-accelerated discontinuous Galerkin methods on hybrid meshes
- Robust benchmarking in noisy environments
- Generalised Summation-by-Parts Operators and Variable Coefficients
- Entropy stable reduced order modeling of nonlinear conservation laws
- On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations