9 papers
Automatic differentiation for performing the Cauchy-Kovalevskaya procedure in Lax-Wendroff type discretizations
Arpit Babbar, Valentin Churavy, Michael Schlottke-Lakemper +1
Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbol…
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…
Admissible Lax-Wendroff Flux Reconstruction Method with Automatic Differentiation on Adaptive Curved Meshes for Relativistic Hydrodynamics
Sujoy Basak, Arpit Babbar, Harish Kumar +1
The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over tim…
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…
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…
Constraints Preserving Lax-Wendroff Flux Reconstruction for Relativistic Hydrodynamics with General Equations of State
Sujoy Basak, Arpit Babbar, Harish Kumar +1
In the realm of relativistic astrophysics, the ideal equation of state with a constant adiabatic index provides a poor approximation due to its inconsistency with relativistic kine…