A dynamically load-balanced parallel $ p $-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation

TL;DR

This paper introduces a dynamic load-balanced parallel p-adaptive flux reconstruction method for turbulence simulation, improving efficiency and reducing computational cost in high-order implicit large eddy simulations.

Contribution

It develops a novel p-adaptive flux reconstruction approach with dynamic load balancing, enabling efficient turbulence simulations with significant computational savings.

Findings

Achieves up to 70% reduction in run time.

Reduces total solution points by up to 76%.

Demonstrates effectiveness in transitional flow simulations.

Abstract

We present a dynamically load-balanced parallel $ p $-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation. The high-order explicit first stage, singly diagonal implicit Runge-Kutta (ESDIRK) method is employed to circumvent the restriction on the time step size. The pseudo transient continuation is coupled with the matrix-free restarted generalized minimal residual (GMRES) method to solve the nonlinear equations at each stage, except the first one, of ESDIRK. We use the spectral decay smoothness indicator as the refinement/coarsening indicator for $ p $-adaptation. A dynamic load balancing technique is developed with the aid of the open-source library ParMETIS. The trivial cost, compared to implicit time stepping, of mesh repartitioning and data redistribution enables us to conduct $ p $-adaptation and load balancing every time step. An isentropic vortex propagation case is employed to study the impact of element weights used in mesh repartitioning on parallel efficiency. We apply the $ p$-adaptive solver for implicit large eddy simulation (ILES) of the transitional flows over a cylinder when Reynolds number (Re) is $ 3900 $ and the SD7003 wing when Re is $ 60000 $. Numerical experiments demonstrate that a significant reduction in the run time (up to $70\%$) and total number of solution points (up to $76\%$) can be achieved with $ p $-adaptation.