A p-multigrid compact gas-kinetic scheme for steady-state acceleration

TL;DR

This paper introduces a p-multigrid technique to accelerate steady-state solutions in a high-order compact gas-kinetic scheme on 3D hybrid meshes, achieving about tenfold speedup in convergence.

Contribution

The paper develops a novel p-multigrid strategy integrated with high-order CGKS for efficient steady-state flow simulations on unstructured meshes.

Findings

Achieved approximately tenfold speedup in convergence rate.

Validated effectiveness in both subsonic and supersonic flows.

Demonstrated applicability in 2D and 3D hybrid unstructured meshes.

Abstract

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a two-level algorithm. On the high-order level, the high-order CGKS is used to evolve both cell-averaged conservative flow variables and their gradients under high-order compact initial reconstruction at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two- and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has be achieved by the approach in comparison with the explicit counterpart.