A hybrid pressure–density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method

Xie, Bin; Deng, Xi; Sun, Ziyao; Xiao, Feng

doi:10.1016/j.jcp.2017.01.043

Cited by 37 publications

(34 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The numerical dissipation errors of evaluation of inviscid flux come from the reconstruction scheme and the Riemann solver [50,51]. A reconstruction scheme higher than second order is not trivial on unstructured grids [52,53].…”

Section: Low Dissipation Riemann Solver With Homogeneous Reconstructimentioning

confidence: 99%

Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet

Deng

Boivin

2020

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

In order to simulate cryogenic H 2 − O 2 jets under subcritical condition, a numerical model is constructed to solve compressible reactive multi-component flows which involve complex multi-physics processes such as moving material interfaces, shock waves, phase transition and combustion. The liquid and reactive gaseous mixture are described by a homogeneous mixture model with diffusion transport for heat, momentum and species. A hybrid thermodynamic closure strategy is proposed to construct an equation of state (EOS) for the mixture. The phase transition process is modeled by a recent fast relaxation method which gradually reaches the thermo-chemical equilibrium without iterative process. A simplified transport model is also implemented to ensure the accurate behavior in the limit of pure fluids and maintain computational efficiency. Last, a 12-step chemistry model is included to account for hydrogen combustion. Then the developed numerical model is solved with the finite volume method where a low dissipation AUSM (advection upstream splitting method) Riemann solver is extended for multi-component flows. A homogeneous reconstruction strategy compatible with the homogeneous mixture model is adopted to prevent numerical oscillations across material interfaces. Having included these elements, the model is validated on a number of canonical configurations, first for multiphase flows, and second for reactive flows. These tests allow recovery of the expected behavior in both the multiphase and reactive limits, and the model capability is further demonstrated on a 2D burning cryogenic H 2 − O 2 jet, in a configuration reminiscent of rocket engine ignition.

show abstract

Section: Low Dissipation Riemann Solver With Homogeneous Reconstructimentioning

confidence: 99%

Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet

Deng

Boivin

2020

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…We use Rusanov scheme (1962) for convection flux and multi-dimensional limiting process (MLP) scheme (Park, Yoon, & Kim, 2010;Xie et al, 2017) is employed for suppressing numerical oscillations. The mesh and density map at final time are given in Figure 6 for both frameworks and density values for the whole field are plotted in Figure 7.…”

Section: Saltzman Problemmentioning

confidence: 99%

“…The other parameters are: γ = 1.4, c v = 2.5, κ = γ c v μ/Pr with Pr = 3 4 . We first performed the inviscid case up to time t = 0.2 with HLL Riemann solver (Harten et al, 1983) for inviscid finite volume flux, and also MLP scheme (Park et al, 2010;Xie et al, 2017) is used for limiting process. The well resolved vortex structures as shown in Figure 8 demonstrate the high fidelity of present method.…”

Section: Viscous Double Mach Reflectionmentioning

confidence: 99%

“…In multi-moment finite volume method, both VIA and PVs are used for local polynomial reconstruction, and simultaneously they are treated as computational variables which are solved by integral form and differential form of the governing equations, respectively. Successive works for Euler equations have been implemented in Xie, Deng, Sun, and Xiao (2017) and . Since the high-order polynomial is based on well-determined local cells, it is straightforward to extend previous studies to moving grids.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An ALE formulation for compressible flows based on multi-moment finite volume method

Jin

Deng

Xiao

2018

Engineering Applications of Computational Fluid Mechanics

Self Cite

View full text Add to dashboard Cite

A direct Arbitrary Lagrangian Eulerian (ALE) formulation using multi-moment finite volume method for viscous compressible flows on unstructured moving grids has been developed and presented in this paper. High-order polynomials are reconstructed over a compact mesh stencil by making use of both volume integrated average value (VIA) and point values (PV) at the vertices of mesh cells which change in time. By formulating the governing equation in ALE integral form and differential form, the computational variables, VIA and PV, are updated, respectively, by a finite volume scheme and a point-wise discretization using multi-moments (VIA and PV). A simple and efficient formulation is derived for moving mesh which satisfies the geometrical conservation law. In the computations involving moving-body, the PVs of velocity at the vertices of cells adjacent to the body surface are coincided with the motion of the body, which eliminates the numerical approximation to find the cell boundary values on the body surface in conventional finite volume method. Numerical tests are presented to verify the present method as a high-order ALE formulation for compressible flows on both stationary and moving grids. ARTICLE HISTORY

show abstract

“…In order to solve these complex flow problems robustly, sharp interface methods must be developed to correctly resolve the interaction of compressible and incompressible flows. Toward this goal, efforts have been made to explore Mach uniform methods based on density-based and pressure-based frameworks [16][17][18][19][20][21][22][23][24][25]. On the one hand, density-based methods can be extended to low Mach number flows using sophisticated spatial discretization method for flows of wide Mach numbers [24].…”

Section: Introductionmentioning

confidence: 99%

Boundary variation diminished conservative semi-Lagrangian method for both compressible and incompressible flows

Xia

Yokoi

et al. 2021

Physics of Fluids

View full text Add to dashboard Cite

show abstract

A hybrid pressure–density-based Mach uniform algorithm for 2D Euler equations on unstructured grids by using multi-moment finite volume method

Cited by 37 publications

References 59 publications

Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet

Diffuse interface modelling of reactive multi-phase flows applied to a sub-critical cryogenic jet

An ALE formulation for compressible flows based on multi-moment finite volume method

Boundary variation diminished conservative semi-Lagrangian method for both compressible and incompressible flows

Contact Info

Product

Resources

About