### 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.

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.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**