A Conservative High-Order Finite Difference Scheme For The Numerical Solution Of The Low Mach-Number Equations

Abstract

A spatially fourth order and temporally third order projection method is proposed for the
numerical solution of the variable-density low-Mach-number approximation of the Navier-stokes equations.
The algorithm is non-dissipative and kinetic energy conserving. These two characteristics are
important in the simulation of turbulent flows, particularly turbulent reacting flows. Another important
feature is that the equation of state is enforced exactly while enforcing the mass conservation constraint.
The projection method requires that a variable coefficient Poisson equation has to be solved at every time
step. Results from model problems will show the spatial and temporal convergence and also the performance
of this algorithm in capturing the physics of the low Mach-number variable-density equations.