Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids

Zhang, Fan; Liu, Jun; Chen, Biaosong

doi:10.1016/j.compfluid.2017.11.019

Cited by 18 publications

(9 citation statements)

References 57 publications

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“…In several points of smooth sine wave, one stencil is removed, and in the unperturbed region, many stencils are removed from final reconstructions due to the round-off errors which activate the cut-off procedure of TENO scheme. The similar behaviour can be found in WENO schemes, as well as the second-order finite volume method which uses limiters that are activated in unperturbed flow field [57]. Tuning the ǫ in Eq.…”

Section: Shock-density Wave Interactionsupporting

confidence: 59%

Detonation Simulations with a Fifth-Order TENO Scheme

Dong¹,

Fu²,

Zhang³

et al. 2019

CICP

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In [Fu et al., JCP 305(2016): 333-359], a family of high-order targeted ENO (TENO) schemes is proposed. The weighting strategy of TENO either applies a candidate stencil with its optimal weight, or removes its contribution completely when it is crossed by discontinuities. This ENO-like stencil selection procedure significantly diminishes the numerical dissipation induced by the nonlinear adaptations of classical WENO schemes. In this paper, the fifth-order TENO scheme is extended to simulate reactive flows in combination with an uncoupled method [1, 2], which splits the reaction source term of detailed chemistry from the flow equations. A set of benchmark cases including the two-dimensional self-sustained detonation is simulated to validate and compare the performance of the fifth-order WENO and TENO schemes. Numerical experiments demonstrate that TENO scheme is robust for simulating chemical reacting flows with using the uncoupled method. In particular, TENO scheme shows better performance in capturing both the shockwaves and the small-scale flow structures, e.g. shear layers and vortices.

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Section: Shock-density Wave Interactionsupporting

confidence: 59%

Detonation Simulations with a Fifth-Order TENO Scheme

Dong¹,

Fu²,

Zhang³

et al. 2019

CICP

Self Cite

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“…The density distributions in the cross section y = 0.5 are shown in Fig.45. Since the limiter has strong influence in the numerical results [44], the results of different spatial reconstructions methods are close. However, in Fig.45, the density profile captured by the present method is slightly sharper than those captured by the other methods.…”

Section: A Mach 3 Wind Tunnel With a Stepmentioning

confidence: 90%

“…where ∆r ik = r k − r i , and φ i ∈ [0, 1] is a slope limiter which is usually employed to suppress oscillations at captured discontinuities [44]. Moreover, the spatial reconstruction procedure in boundary cells and faces is to be specifically discussed in the following sections.…”

Section: Governing Equations and The Discretizationmentioning

confidence: 99%

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An iterative near-boundary reconstruction strategy for unstructured finite volume method

Chen

Zhang

Liu

et al. 2020

Journal of Computational Physics

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Near-boundary approximation of the second-order cell-centered unstructured finite volume method is investigated and improved to avoid accuracy loss. In this work, an iterative strategy is proposed, combining with a vertex-based weighted least squares gradient reconstruction method, which is more accurate and efficient than several conventional methods. In the present approach, the solutions at boundary surfaces and the gradients in boundary cells are iteratively updated, to minimize overall numerical errors. In the meantime, a vectorial limiter is implemented to guarantee the correctness of the iterative process, and physical properties of boundaries are taken into account to correctly attain physical results. A series of numerical test cases show that the present method significantly reduces the error of near-boundary approximations. Moreover, since the iterative scheme is only activated for near-boundary solutions, the minor extra computational effort does not damage the overall performance of the solver.

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“…The computation of the convective fluxes of the two-fluid equations is based on the Lax-Friedrichs scheme. The spatial derivatives of primitive variables, including density ( ), velocity (v) and temperature (T ), are calculated using the Weighted Least SQuares (WLSQ) linear reconstruction for unstructured grids, resulting in a second-order accurate spatial discretization, and the Barth-Jespersen limiter (Barth & Jespersen 1989) is applied with a strict limiting criterion (Zhang 2017;Zhang et al 2018) to guarantee the robustness of shock-capturing computation in the present gravitationally stratified media where smooth acoustic waves may steepen to shocks. The resulting sparse algebraic system is solved by using the Generalized Minimal RESidual (GMRES) method (Saad & Schultz 1986) with the restricted additive Schwarz preconditioner (Widlund & Dryja 1987), and the methods are provided by the Portable, Extensible Toolkit for Scientific computation (PETSc) 2 .…”

Section: Numerical Schemesmentioning

confidence: 99%

Two-fluid Modeling of Acoustic Wave Propagation in Gravitationally Stratified Isothermal Media

Zhang

Poedts

Lani

et al. 2021

ApJ

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To study acoustic wave propagation and the corresponding energy deposition in partially ionized plasmas, we use a two-fluid computational model which treats neutrals and charged particles (electrons and ions) as two separate fluids. This two-fluid model takes into account the ion-neutral collisions, ionization and recombination, allowing us to investigate both the collisional and reactive interactions between uncoupled ions and neutrals in the plasmas. In the present numerical simulations, the initial density is specified to reach hydrostatic equilibrium, and as a comparison, chemical equilibrium is also taken into account to provide a density profile that differs from typical hydrostatic equilibrium profiles. External velocity drivers are then imposed to generate monochromatic acoustic waves. As it is well known, the upwards propagating acoustic waves steepen in gravitationally stratified plasmas due to the exponentially decreasing density, and they heat the plasmas in the nonlinear regimes where kinetic energy is dissipated by shock waves and collisional interactions. In particular, the lower ionization fraction resulting from the present initial chemical equilibrium significantly enhances the heating efficiency. Moreover, the ionization process absorbs a significant amount of energy, and the decoupling between ions and neutrals is also enhanced while considering ionization and recombination. Therefore, simulations without considering ionization and recombination may overestimate the overall heating effects but also underestimate the energy dissipation. The results also suggest that a more accurate ionization and recombination model could be essential for improving the modelling of partially ionized plasmas.

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Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids

Cited by 18 publications

References 57 publications

Detonation Simulations with a Fifth-Order TENO Scheme

Detonation Simulations with a Fifth-Order TENO Scheme

An iterative near-boundary reconstruction strategy for unstructured finite volume method

Two-fluid Modeling of Acoustic Wave Propagation in Gravitationally Stratified Isothermal Media

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