Admissible Lax-Wendroff Flux Reconstruction Method with Automatic Differentiation on Adaptive Curved Meshes for Relativistic Hydrodynamics
This work addresses computational efficiency and accuracy in simulating relativistic hydrodynamics for applications like astrophysics, but it is incremental as it builds on existing methods with specific enhancements.
The authors tackled the challenge of solving relativistic hydrodynamics equations with sharp structures by developing an adaptive mesh refinement scheme using a high-order Lax-Wendroff flux reconstruction method, which incorporates automatic differentiation for Jacobian-free computations and blending with a low-order method to control oscillations, achieving robust and accurate simulations in test cases with high Lorentz factors and discontinuities.
The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over time. Capturing these sharp waves effectively requires a mesh with high resolution, making the scheme computationally expensive. In this work, adaptive mesh refinement is used with the high-order Lax-Wendroff flux reconstruction (LWFR) method to solve the system of RHD equations, which is closed with general equations of state. To make the scheme Jacobian-free, the idea of automatic differentiation is incorporated for computing the temporal derivatives in the time average flux approximations. The high-order method is blended with an admissible low-order method at the subcell level to control the Gibbs oscillations and maintain the physical admissibility of the solution. Finally, several test cases involving high Lorentz factors, low densities, low pressures, strong shock waves, and other discontinuities are used to demonstrate the robustness, accuracy, and effectiveness of the proposed method. These simulations are performed with AMR using various linear and curved meshes to show the scheme's efficiency and ability to handle complex geometries.