A new highly scalable, high-order accurate framework for variable-density flows: Application to non-Boussinesq gravity currents

Abstract

This paper introduces a new code "QuasIncompact3D" for solving the variabledensity Navier-Stokes equations in the low-Mach number limit. It is derived from the Incompact3D framework which is designed for incompressible flows [1]. QuasIncompact3D is based on high-order accurate compact finite-differences [2], an efficient 2D domain decomposition [3] and a spectral Poisson solver. The first half of the paper focuses on introducing the low-Mach number governing equations, the numerical methods and the algorithm employed by QuasIncompact3D to solve them. Two approaches to forming the pressure-Poisson equation are presented: one based on an extrapolation that is efficient but limited to low density ratios and another one using an iterative approach suitable for higher density ratios. The scalability of QuasIncompact3D is demonstrated on several TIER-1/0 supercomputers using both approaches, showing good scaling up to 65k cores.

High-fidelity simulations of gravity currents using a high-order finite-difference spectral vanishing viscosity approach

“…Our next study will focus on high-fidelity simulations of high Reynolds numbers Boussinesq gravity currents, thanks to the flow solver QuasIncompact3D, part of the Xcompact3d framework. This solver is based on the compressible Navier-Stokes equations in the low Mach number limit, allowing simulations of gravity currents with densities ratio of up to 10 between the heavy release and the ambient fluid (Bartholomew and Laizet, 2019). High Reynolds numbers non-Boussinesq gravity currents in a basin set-up (where the current can freely evolve in the spanwise and streamwise directions, see Francisco et al (2018)) will also be investigated.…”

“…The flow solvers within Xcompact3D can scale well with up to hundreds of thousands of MPI-processes for simulations with several billion mesh nodes (Laizet and Li, 2011). The Xcompact3D framework has been used recently to perform DNS of Boussinesq gravity currents in various set-up and for a wide range of Reynolds numbers (Espath et al, 2014(Espath et al, , 2015Francisco et al, 2018;Lucchese et al, 2019) and DNS of non-Boussinesq gravity currents (Bartholomew and Laizet, 2019). Finally, further validation and verification studies of the code for the SVV model and the explicit LES models can be found in: Dairay et al (2014Dairay et al ( , 2017; Ioannou and Laizet (2018); Deskos et al (2019); Schuch et al (2018); Deskos et al (2020).…”

Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh

“…As shown in (1)-( 5) under the LMN approximation the pressure field may be decomposed into the thermodynamic p (0) , and mechanical p (1) pressures. The former is constant in space which allows filtering of the acoustic pressure waves from the solution, whilst the mechanical pressure behaves as the pressure field of an incompressible flow; for further details the interested reader is referred to [3][4][5]. This formulation allows Xcompact3D to tackle flows with variable density in the regime 0 ≤ M ≲ 0.3 where M is the Mach number.…”

Digital 3D Animation of Powder-Snow Avalanches

“…For powder-snow avalanches, the difference between powder-snow and air densities invalidates the Boussinesq assumption (HOPFINGER, 1983). Non-Boussinesq 15 models for gravity currents can be found in (BIRMAN; MEIBURG, 2006;LAIZET, 2019).…”