A dimensionally split Cartesian cut cell method for the compressible Navier-Stokes equations

TL;DR

This paper introduces a novel dimensionally split Cartesian cut cell method for solving the compressible Navier-Stokes equations, achieving second-order accuracy and good performance across various flow regimes.

Contribution

It presents the first dimensionally split cut cell method for the compressible Navier-Stokes equations, with detailed 3D implementation and validation.

Findings

Achieves second-order accuracy in L1 norm

Demonstrates good agreement with theoretical and experimental results

Handles a range of flow regimes from nearly incompressible to highly compressible

Abstract

We present a dimensionally split method for computing solutions to the compressible Navier-Stokes equations on Cartesian cut cell meshes. The method is globally second order accurate in the L1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a number of test problems ranging from the nearly incompressible to the highly compressible flow regimes. All the computed results show good agreement with reference results from theory, experiment and previous numerical studies. To the best of our knowledge, this is the first presentation of a dimensionally split cut cell method for the compressible Navier-Stokes equations in the literature.