A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system

Boscarino, Sebastiano; Qiu, Jing-Mei; Russo, Giovanni; Xiong, Tao

doi:10.1016/j.jcp.2019.04.057

Cited by 41 publications

(70 citation statements)

References 57 publications

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“…and appropriate boundary conditions [3,4], e.g., periodic, wall or homogeneous Neumann boundary conditions. Taking the divergence of the first equation in (5) and using the incompressibility, we obtain…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, some all-speed schemes [3,4,7,8,9] have been derived for the compressible-incompressible limit problems based on the idea of the asymptoticpreserving (AP) methodology introduced by Jin [10,11] for relaxation systems. The AP all-speed schemes are uniformly consistent with the low-Mach number limit and are uniformly stable.…”

Section: Introductionmentioning

confidence: 99%

“…The implicit strategies avoid the CFL restriction, but they need to solve highly nonlinear equations and add an excessive numerical dissipation to the slow wave, degrading the accuracy of the method [3]. To overcome the drawbacks, the semi-implicit or implicit-explicit (IMEX) time discretization strategies are widely applied based on the acoustic/advection splitting of the Euler equations into the stiff/non-stiff parts (or fast and slow fluxes) [4,5,7,9,12,13,14,15,16]. These strategies treat with the stiff part implicitly and the non-stiff part explicitly to solve the isentropic Euler equations effectively and efficiently.…”

Section: Introductionmentioning

confidence: 99%

“…These strategies treat with the stiff part implicitly and the non-stiff part explicitly to solve the isentropic Euler equations effectively and efficiently. The IMEX time discretization combined with the shock-capturing schemes, e.g., the first-order local Lax-Friedrichs (or Rusanov) scheme [5], the second-order finite volume method [3,17], the arbitrary high order accurate discontinuous Galerkin method [18] and the fifth-order finite difference weighted essentially non-oscillatory (WENO) scheme [4] has been shown its good performances in compressible and incompressible regimes.…”

Section: Introductionmentioning

confidence: 99%

“…Compared to the WENO schemes, the WCNS's feature a better spectral resolution at the same order of accuracy and are more flexible in the choice of flux splitting methods and flux derivatives can be computed by different explicit or implicit compact finite difference methods [21]. In this work, in view of the good performance of the IMEX time discretization method and the WCNS's, we design a high order IMEX WCNS for the all-Mach isentropic Euler system based on the acoustic/advection splitting strategy [4]. The stiff linear part governing fast acoustic and the non-stiff nonlinear part modeling slow nonlinear advection effects are solved by the high order implicit and explicit time discretization methods, respectively.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

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The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe CFL restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization and a fifth-order WCNS is used for the spatial discretization. The designed semi-implicit WCNS is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Jiang

Chen

Zhang

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

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Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

et al. 2021

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In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.

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Asymptotic Preserving Low Mach Number Accurate IMEX Finite Volume Schemes for the Isentropic Euler Equations

Arun

Samantaray

2020

J Sci Comput

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In this paper the analysis of an asymptotic preserving (AP) IMEX-RK finite volume scheme for the wave equation system in the zero Mach number limit is presented. The accuracy of a numerical scheme at low Mach numbers is its ability to maintain the solution close to the incompressible solution for all times, and this can be formulated in terms of the invariance of a space of constant densities and divergence-free velocities. An IMEX-RK methodology is employed to obtain a time semi-discrete scheme, and a space-time fully-discrete scheme is derived by using standard finite volume techniques. The existence of a unique numerical solution, its uniform stability with respect to the Mach number, the AP property, and the accuracy at low Mach numbers are established for both time semi-discrete, and space-time fully-discrete schemes. Extensive numerical case studies confirm uniform second order convergence of the scheme with respect to the Mach number, and all the above-mentioned properties.

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A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system

Cited by 41 publications

References 57 publications

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

Asymptotic Preserving Low Mach Number Accurate IMEX Finite Volume Schemes for the Isentropic Euler Equations

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