A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state

Ward, G. M.; Pullin, D. I.

doi:10.1016/j.jcp.2009.12.027

Cited by 19 publications

(15 citation statements)

References 33 publications

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“…Some authors have proposed partly alleviating this problem by either reducing the order of the reconstruction [42] or utilizing flux limiters [53–55] in the affected regions of the flow. This, however, may lead to excessive smearing of material interfaces as they evolve or, in the case that an interface-sharpening technique is employed as a remedy, a loss of discrete conservation [54].…”

Section: Methodsmentioning

confidence: 99%

Finite-volume WENO scheme for viscous compressible multicomponent flows

Coralic¹,

Colonius²

2014

Journal of Computational Physics

189

239

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We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin.

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Section: Methodsmentioning

confidence: 99%

Finite-volume WENO scheme for viscous compressible multicomponent flows

Coralic¹,

Colonius²

2014

Journal of Computational Physics

189

239

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“…The use of oscillation-free single fluid discretization schemes for numerical simulation of multiphase compressible flows is an effective and well established strategy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. These schemes use enforcement of appropriate constraints across the diffuse material interface (such as preservation of pressure and normal velocity continuity (cf.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

Shukla

2014

Journal of Computational Physics

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“…26,30,33 In addressing this issue, we have developed a hybrid methodology that combines a kinetic-energy preserving center-difference approach 34 with a Roe linearized Riemann solver 26 by way of a local smoothness dependent limiter. 6 In brief, a numerical derivative operator is defined by a difference of reconstructed quantities…”

Section: Mie-grü Neisen Mixturementioning

confidence: 99%

“…Temporal discretization is achieved by thirdorder total variation diminishing (TVD) Runge-Kutta. 35 Code verification for manufactured simple wave solutions was performed, 6 demonstrating fourth-order spatial convergence. Implementation of the solver has been performed utilizing the California Institute of Technology's VTF AMROC 4,5,27 software with adaptive mesh refinement (AMR) capability.…”

Section: Mie-grü Neisen Mixturementioning

confidence: 99%

“…24 Presently, we utilize a solver that was developed to address such numerical challenges created by Mie-Grüneisen equation of state. 6 The solver combines a low dissipation, skew-symmetric, kinetic-energy preserving, and center-difference method with a Roe-Riemann solver to provide efficient treatment of smooth and sharp flow features. To avoid ill-posed vortex sheets associated with truly discontinuous interfaces, 25 we use a fluidmixture like approach for multiphase Mie-Grüneisen flows.…”

Section: Introductionmentioning

confidence: 99%

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A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Ward¹,

Pullin

2011

Physics of Fluids

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We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970) (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related byComparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer's linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.

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A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state

Cited by 19 publications

References 33 publications

Finite-volume WENO scheme for viscous compressible multicomponent flows

Finite-volume WENO scheme for viscous compressible multicomponent flows

Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

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