A fully conservative discrete velocity Boltzmann solver with parallel adaptive mesh refinement for compressible flows

Abstract

This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population quasi-equilibrium Bhatnagar-Gross-Krook discrete velocity Boltzmann model. A validation has shown that conservation laws are strictly preserved through the application of refluxing operations at coarse-fine interfaces. Moreover, the targeted macroscopic moments of Euler and Navier-Stokes-Fourier level flows were accurately recovered with correct and Galilean invariant dispersion rates for a temperature range over three orders of magnitude and dissipation rates of all eigen-modes up to Mach of order 1.8. Results for one- and two-dimensional benchmarks up to Mach numbers of 3.2 and temperature ratios of 7, such as the Sod and Lax shock tubes, the Shu-Osher and several Riemann problems, as well as viscous shock-vortex interactions, have demonstrated that the solver precisely captures reference solutions. Excellent performance in obtaining sensitive quantities was proven, for example in the test case involving nonlinear acoustics, whilst, for the same accuracy and fidelity of the solution, the AMR methodology significantly reduced computational cost and memory footprints. Over all demonstrated two-dimensional problems, up to a 4- to 9-fold reduction was achieved and an upper limit of the AMR overhead of 30% was found in a case with very cost-intensive parameter choice. The proposed solver marks an accurate, efficient and scalable framework for kinetic simulations of compressible flows with moderate supersonic speeds and discontinuities, offering a valuable tool for studying complex problems in fluid dynamics.