An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems

Shyue, Keh‐Ming

doi:10.1006/jcph.1998.5930

Cited by 339 publications

(375 citation statements)

References 63 publications

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“…If the conservative variable ρα is used, higher order schemes of shock capturing applied to multicomponent flows can produce oscillations at the interface of different fluids (Shyue 1998;Johnsen & Colonius 2006).…”

Section: Euler Equations In Laboratory Framementioning

confidence: 99%

Simulation of the growth of the 3D Rayleigh-Taylor instability in supernova remnants using an expanding reference frame

Fraschetti

Teyssier

Ballet³

et al. 2010

A&A

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Context. The Rayleigh-Taylor instabilities that are generated by the deceleration of a supernova remnant during the ejecta-dominated phase are known to produce finger-like structures in the matter distribution that modify the geometry of the remnant. The morphology of supernova remnants is also expected to be modified when efficient particle acceleration occurs at their shocks. Aims. The impact of the Rayleigh-Taylor instabilities from the ejecta-dominated to the Sedov-Taylor phase is investigated over one octant of the supernova remnant. We also study the effect of efficient particle acceleration at the forward shock on the growth of the Rayleigh-Taylor instabilities. Methods. We modified the Adaptive Mesh Refinement code RAMSES to study with hydrodynamic numerical simulations the evolution of supernova remnants in the framework of an expanding reference frame. The adiabatic index of a relativistic gas between the forward shock and the contact discontinuity mimics the presence of accelerated particles. Results. The great advantage of the super-comoving coordinate system adopted here is that it minimizes numerical diffusion at the contact discontinuity, since it is stationary with respect to the grid. We propose an accurate expression for the growth of the RayleighTaylor structures that smoothly connects the early growth to the asymptotic self-similar behaviour. Conclusions. The development of the Rayleigh-Taylor structures is affected, although not drastically, if the blast wave is dominated by cosmic rays. The amount of ejecta that reaches the shocked interstellar medium is smaller in this case. If acceleration were to occur at both shocks, the extent of the Rayleigh-Taylor structures would be similar but the reverse shock would be strongly perturbed.

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Section: Euler Equations In Laboratory Framementioning

confidence: 99%

Simulation of the growth of the 3D Rayleigh-Taylor instability in supernova remnants using an expanding reference frame

Fraschetti

Teyssier

Ballet³

et al. 2010

A&A

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“…The fluid components are identified by the variable φ, which may be taken to be a state variable, for example, the specific heat ratio γ [37] (see also [24]), or any function of γ (e.g., φ = 1 γ−1 was advocated in [2], and extended to stiff gases in [38][39][40]). Related models take φ to be the mass fraction of the fluid component in the fluid mixture [1,2,6,31], or a level-set function, whose zero level-set defines the interface between the fluid components [10,11,34].…”

Section: Introductionmentioning

confidence: 99%

Interface tracking method for compressible multifluids

2008

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Abstract. This paper is concerned with numerical methods for compressible multicomponent fluids.The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a "mixed-cell" EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell information by solving the Riemann problem between its single-fluid neighboring cells. The resulting algorithm is oscillation-free for isolated material interfaces, conservative, and tends to produce almost perfect jumps across material fronts. The computational framework is general and may be used in conjunction with one's favorite finite-volume method. The robustness of the method is illustrated on shock-interface interaction in one space dimension, oscillating bubbles with radial symmetry and shock-bubble interaction in two space dimensions.Mathematics Subject Classification. 76M12, 76N15, 35L65, 35L67.

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“…When the bubble explodes under the water, there are an outgoing shock wave in the water and an incoming rarefaction wave in the water. It can be easily observed that the contours of density and pressure by our method are captured symmetrically and better than those in the work of Shyue [4]. Besides, the profiles along y D 0:5 are also plotted in Figures 10 and 11.…”

Section: Advection Of a Gas-gas Interface Problemmentioning

confidence: 75%

“…Hence, many methods [1][2][3][4][5][6][7] have been developed to model and simulate them. Among them, the front capturing method is very promising for its efficiency and simplicity when dealing with different fluids.…”

Section: Introductionmentioning

confidence: 99%

An improved unstructured WENO method for compressible multi‐fluids flow

Zheng

Zhao

2016

Numerical Methods in Fluids

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SUMMARYAn improved high-order accurate WENO finite volume method based on unstructured grids for compressible multi-fluids flow is proposed in this paper. The third-order accuracy WENO finite volume method based on triangle cell is used to discretize the governing equations. To have higher order of accuracy, the P1 polynomial is reconstructed firstly. After that, the P2 polynomial is reconstructed from the combination of the P1. The reconstructed coefficients are calculated by analytical form of inverse matrix rather than the numerical inversion. This greatly improved the efficiency and the robustness. Four examples are presented to examine this algorithm. Numerical results show that there is no spurious oscillation of velocity and pressure across the interface and high-order accurate result can be achieved.

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An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems

Cited by 339 publications

References 63 publications

Simulation of the growth of the 3D Rayleigh-Taylor instability in supernova remnants using an expanding reference frame

Simulation of the growth of the 3D Rayleigh-Taylor instability in supernova remnants using an expanding reference frame

Interface tracking method for compressible multifluids

An improved unstructured WENO method for compressible multi‐fluids flow

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