A Relaxation Scheme for the Simulation of Low Mach Number Flows

Abbate, Emanuela; Iollo, Angelo; Puppo, Gabriella

doi:10.1007/978-3-319-57394-6_25

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…We present the all-speed relaxation scheme recently introduced in [1,32]. The scheme is the same for all the considered compressible materials, since it does not have a direct dependence on the state law.…”

Section: Implicit All-speed Schemementioning

confidence: 99%

An Implicit Scheme for Moving Walls and Multi-Material Interfaces in Weakly Compressible Materials

Abbate¹

2020

CiCP

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We propose a numerical method for the simulation of flows from weakly compressible to low Mach regimes in domains with moving boundaries. Non-miscible weakly compressible materials separated by an interface are included as well. The scheme is fully implicit and it exploits the relaxation all-speed scheme introduced in [1]. We consider media with significantly different physical properties and constitutive laws, as fluids and hyperelastic solids. The proposed numerical scheme is fully Eulerian and it is the same for all materials. We present numerical validations by simulating weakly compressible fluid/fluid, solid/solid and solid/fluid interactions.

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Section: Implicit All-speed Schemementioning

confidence: 99%

An Implicit Scheme for Moving Walls and Multi-Material Interfaces in Weakly Compressible Materials

Abbate¹

2020

CiCP

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“…The function f (M loc ) has to satisfy 0 ≤ f (M loc ) ≤ 1 (in the numerical experiments we choose f (M loc ) = min{1, M loc }) and M loc is computed at the previous time step at the numerical interface x i+1/2,j . This allows to recover the correct numerical viscosity for each considered regime [2,3].…”

Section: Low Mach Number Asymptoticsmentioning

confidence: 99%

An Asymptotic-Preserving All-Speed Scheme for Fluid Dynamics and Nonlinear Elasticity

Abbate¹,

Iollo²,

Puppo³

2019

SIAM J. Sci. Comput.

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An implicit relaxation scheme is derived for the simulation of multi-dimensional flows at all Mach numbers, ranging from very small to order unity. An analytical proof of the asymptotic preserving property is proposed and the divergence-free condition on the velocity in the incompressible regime is respected. The scheme possesses a general structure, which is independent of the considered state law and thus can be adopted to solve gas and fluid flows, but also deformations of elastic solids. This is achieved by adopting the Jin-Xin relaxation technique in order to get a linear transport operator. The spatial derivatives are thus independent of the EOS and an easy implementation of fully implicit time discretizations is possible. Several validations on multi-dimensional tests are presented, showing that the correct numerical viscosity is recovered in both the fully compressible and the low Mach regimes. An algorithm to perform grid adaptivity is also proposed, via the computation of the entropy residual of the scheme.

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A Relaxation Scheme for the Simulation of Low Mach Number Flows

Cited by 2 publications

References 8 publications

An Implicit Scheme for Moving Walls and Multi-Material Interfaces in Weakly Compressible Materials

An Implicit Scheme for Moving Walls and Multi-Material Interfaces in Weakly Compressible Materials

An Asymptotic-Preserving All-Speed Scheme for Fluid Dynamics and Nonlinear Elasticity

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