A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics

Barsukow, Wasilij; Edelmann, P. V. F.; Klingenberg, Christian; Miczek, Fabian; Röpke, F. K.

doi:10.1007/s10915-017-0372-4

Cited by 45 publications

(46 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As it is well-known in literature, we get the modified equation ∂ t u + µ∂ x u = D∂ xx u. Here µ is the speed of the wave (for system (17) is defined in (21)). The diffusion coefficient D for the explicit-upwind scheme is the following:…”

Section: Numerical Viscositymentioning

confidence: 99%

“…A possible approach consists in choosing implicit time discretizations, which allow to avoid the acoustic CFL constraint. Several preconditioning techniques have been devised to decrease the numerical diffusion of upwind schemes at low Mach numbers in such implicit methods [14,15,16,17], starting from the "artificial compressibility" technique of Chorin [18] and from Turkel's work [19,20]. However, it is extremely difficult to handle the non-linearities of classical upwind discretizations (e.g.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An all-speed relaxation scheme for gases and compressible materials

Abbate

Iollo

Puppo

2017

Journal of Computational Physics

View full text Add to dashboard Cite

We present a novel relaxation scheme for the simulation of compressible material flows at all speeds. An Eulerian model describing gases, fluids and elastic solids with the same system of conservation laws is adopted. The proposed numerical scheme is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in all different Mach regimes. The scheme is validated by simulating gas and liquid flows with different Mach numbers. The simulation of the deformation of compressible solids is also approached, assessing the ability of the scheme in approximating material waves in hyperelastic media.

show abstract

Section: Numerical Viscositymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An all-speed relaxation scheme for gases and compressible materials

Abbate

Iollo

Puppo

2017

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…For historical reasons, these modifications have been called flux preconditioning. In this paper D will be called a modified diffusion or upwinding matrix, consistently with [2]. The particular choice in [23] is D = P −1 |P A| with P …”

Section: Modifications Of Diffusion Matrices In Roe-type Methodsmentioning

confidence: 99%

“…Stability of such iterated linear maps needs all its eigenvalues to be less than 1 in absolute value. A detailed stability analysis is performed in [2]. Evaluating the limit M → 0 for the suggested upwinding matrix yields…”

Section: Stability With Explicit Time Integrationmentioning

confidence: 99%

A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms

et al. 2017

Self Cite

View full text Add to dashboard Cite

Abstract. In order to perform simulations of low Mach number flow in presence of gravity the technique from [23] is found insufficient as it is unable to cope with the presence of a hydrostatic equilibrium. Instead, a new modification of the diffusion matrix in the context of Roe-type schemes is suggested. We show that without gravity it is able to resolve the incompressible limit, and does not violate the conditions of hydrostatic equilibrium when gravity is present. These properties are verified by performing a formal asymptotic analysis of the scheme. Furthermore, we study its von Neumann stability when subject to explicit time integration and demonstrate its abilities on numerical examples.

show abstract

“…To resolve the small dynamics on the hydrostatic background it can be necessary to use so-called low Mach number numerical flux functions (e.g. [2,30]). These can be used in combination with our wellbalanced method to obtain a finite volume scheme which is both well-balanced and capable of resolving low Mach number fluxes.…”

Section: Introductionmentioning

confidence: 99%

Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems

Berberich¹

2019

CICP

View full text Add to dashboard Cite

We develop a second order well-balanced finite volume scheme for compressible Euler equations with a gravitational source term. The well-balanced property holds for arbitrary hydrostatic solutions of the corresponding Euler equations without any restriction on the equation of state. The hydrostatic solution must be known a priori either as an analytical formula or as a discrete solution at the grid points. The scheme can be applied on curvilinear meshes and in combination with any consistent numerical flux function and time stepping routines. These properties are demonstrated on a range of numerical tests. † By the term time-stepping routines we refer to ODE solvers which are applied to evolve the semi-discrete scheme obtained after spatial discretization by a finite volume method.

show abstract

A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics

Cited by 45 publications

References 34 publications

An all-speed relaxation scheme for gases and compressible materials

An all-speed relaxation scheme for gases and compressible materials

A low-Mach Roe-type solver for the Euler equations allowing for gravity source terms

Second Order Finite Volume Scheme for Euler Equations with Gravity which is Well-Balanced for General Equations of State and Grid Systems

Contact Info

Product

Resources

About