Decoupling schemes for predicting compressible fluid flows

TL;DR

This paper presents decoupling schemes for simulating compressible fluid flows using Euler equations, focusing on conservation laws and employing splitting methods with iterative solutions, demonstrated through 2D numerical experiments.

Contribution

It introduces novel decoupling schemes employing splitting methods and iterative linearized solutions for compressible fluid flow simulation, emphasizing conservation properties.

Findings

Schemes effectively preserve mass and energy conservation.

Numerical results demonstrate stability and accuracy in 2D models.

Decoupling improves computational efficiency without sacrificing accuracy.

Abstract

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the density. An approximate solution of an initial--boundary value problem is calculated using the finite element approximation in space. The fully implicit two-level scheme is used for discretization in time. Numerical implementation is based on Newton's method. The main attention is paid to fulfilling conservation laws for the mass and total mechanical energy for the discrete formulation. Two-level schemes of splitting by physical processes are employed for numerical solving problems of barotropic fluid flows. For a transition from one time level to the next one, an iterative process is used, where at each iteration the linearized scheme is implemented via solving individual problems for the density and velocity. Possibilities of the proposed schemes are illustrated by numerical results for a two--dimensional model problem with density perturbations.