Efficient parallel solver for rarefied gas flow using GSIS

TL;DR

This paper introduces a scalable parallel solver based on GSIS for three-dimensional rarefied gas flows, achieving rapid convergence and high accuracy for complex hypersonic problems with billions of grid points.

Contribution

It extends GSIS to large-scale 3D problems with a parallel computing strategy, enabling efficient simulation of hypersonic flows with billions of grids.

Findings

Achieved convergence within one hour for complex hypersonic flows.

Successfully handled up to 100 billion spatial and velocity grids.

Demonstrated efficiency and accuracy in 3D rarefied gas flow simulations.

Abstract

Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead to the significant reduction of iteration numbers and spatial cells in the near-continuum flow regime. However, the efficiency and accuracy of GSIS has only been demonstrated in two-dimensional problems with small numbers of spatial cells and discrete velocities. Here, a large-scale parallel computing strategy is designed to extend the GSIS to three-dimensional flow problems, including the supersonic flows which are usually difficult to solve by the discrete velocity method. Since the GSIS involves the calculation of the mesoscopic kinetic equation which is defined in six-dimensional phase-space, and the macroscopic high-temperature Navier-Stokes-Fourier equations in three-dimensional physical space, the proper partition of the spatial and velocity spaces, and the allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys to improving the overall computational efficiency. These factors are systematically tested to achieve optimal performance, up to 100 billion spatial and velocity grids. For hypersonic flows around the Apollo reentry capsule, the X38-like vehicle, and the space station, our parallel solver can obtain the converged solution within one hour.