A weakly-compressible Cartesian grid approach for hydrodynamic flows

Bigay, P.; Oger, G.; Guilcher, Pierre-Michel; Touzé, David Le

doi:10.1016/j.cpc.2017.06.010

Cited by 16 publications

(4 citation statements)

References 34 publications

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“…The flow F is more efficient to resolve than the F because the disparity between the velocity of the fluid and the velocity of acoustic waves is reduced. This is the essence of weakly compressible (WC) methods, in which the compressible Navier-Stokes equations are used to simulate incompressible or almost compressible flows [23,27,7]. However, the flow F may only approximate the flow F in the nondimensionalised sense, since it necessarily has a different time scale t b = t b /α, velocity scale U b = αU b , density scale ρ b = ρ b /α and pressure scale P b = P b /α and thus requires adjusted initial and boundary conditions.…”

Section: Derivation Of the Artificial Pressure Equationsmentioning

confidence: 99%

Analysis of artificial pressure equations in numerical simulations of a turbulent channel flow

Dupuy

Toutant

Bataille

2020

Journal of Computational Physics

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Recently, several methods have been proposed to simulate incompressible fluid flows using an artificial pressure evolution equation, avoiding the resolution of a Poisson equation. These methods can be seen as various levels of approximation of the compressible Navier-Stokes equation in the low Mach number limit. We study the simulation of incompressible wall-bounded flows using several artificial pressure equations in order to determine the most relevant approximations. The simulations are stable using a finite difference method in a staggered grid system, even without diffusive term, and converge to the incompressible solution, both in direct numerical simulations and for coarser meshes, to be used in large-eddy simulations. A pressure equation with a convective and a diffusive term produces a more accurate solution than a compressible solver or methods involving more approximations. This suggests that it is near to an optimal level of approximation. The presence of a convective term in the pressure evolution equation is in particular crucial for the accuracy of the method. The rate of convergence of the solution in terms of artificial Mach number is studied numerically and validates the theoretical quadratic convergence rate. We demonstrate that this property can be used to accelerate the rate of convergence using an extrapolation in terms of artificial Mach number. Since the approach is based on an explicit and local system of equations, the numerical procedure is massively parallelisable and has low memory requirements.

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Section: Derivation Of the Artificial Pressure Equationsmentioning

confidence: 99%

Analysis of artificial pressure equations in numerical simulations of a turbulent channel flow

Dupuy

Toutant

Bataille

2020

Journal of Computational Physics

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“…where γ = α 1 /(1 − α 1 ), q = ρ 2,0 c 2 2 − ρ 1,0 c 2 1 and q = ρ2 c 2 2 − ρ1 c 2 1 . Given ρ1 > 0 and ρ2 > 0, this quadratic equation (5) possesses two real solutions…”

Section: Equilibrium Volume Fractionmentioning

confidence: 99%

“…). Because of the explicit feature of the scheme, the time-step ∆t is chosen as [5] ∆t = CFL min e (∆x, ∆y)…”

Section: Finite Volume Formulationmentioning

confidence: 99%