An all-speed relaxation scheme for gases and compressible materials

Abbate, Emanuela; Iollo, Angelo; Puppo, Gabriella

doi:10.1016/j.jcp.2017.08.052

Cited by 18 publications

(58 citation statements)

References 43 publications

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“…thus having µ 1 ≥ max|u − c|, µ 2 = µ 3 ≥ max|u| and µ 4 ≥ max|u + c| for the Euler system (for more details on the construction of the relaxation matrices see [2]). We remark that the relaxation is performed direction by direction, namely the equations on the relaxation variables are one dimensional problems.…”

Section: Low Mach Number Asymptoticsmentioning

confidence: 99%

“…Scheme (3.9) is fully implicit, thus unconditionally stable (see [2]). Nevertheless, ∆t has to be chosen accordingly to the desired accuracy.…”

Section: Low Mach Number Asymptoticsmentioning

confidence: 99%

“…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%

“…To this end, we adopt a monolithic Eulerian model describing different materials with the same system of conservation laws. The model derivation has been exstensively discussed in several previous works [19,37,20,2].…”

Section: Adaptive Mesh Refinementmentioning

confidence: 99%

“…In the present work, our interest is the numerical simulation of flows with Mach numbers ranging from the incompressible limit to compressible regimes with M O (1). To this end, we have derived in [2] an implicit all-speed scheme, which is here extended for the accurate solution of multi-dimensional flows. Moreover, its AP property is proved analytically and numerically.…”

mentioning

confidence: 99%

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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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Section: Low Mach Number Asymptoticsmentioning

confidence: 99%

“…Scheme (3.9) is fully implicit, thus unconditionally stable (see [2]). Nevertheless, ∆t has to be chosen accordingly to the desired accuracy.…”

Section: Low Mach Number Asymptoticsmentioning

confidence: 99%

Section: Low Mach Number Asymptoticsmentioning

confidence: 99%

Section: Adaptive Mesh Refinementmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

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

Abbate¹,

Iollo²,

Puppo³

2019

SIAM J. Sci. Comput.

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A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium

Abgrall

2022

Numerical Methods in Fluids

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Within the framework of diffuse interface methods, we derive a pressure-based Baer-Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user-defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of nonconservative terms involving the gradient of the volume fraction fulfills by construction the nondisturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one-dimensional simulations of shock-tube and Riemann-problems, involving water-aluminum and water-air mixtures, vapor-liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state-stiffened gas and Peng-Robinson-were investigated.

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