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作者:Jingwei Hu , Xiangxiong Zhang
来源:[J].Journal of Scientific Computing(IF 1.71), 2017, Vol.73 (2-3), pp.797-818
摘要:Implicit–explicit (IMEX) Runge–Kutta (RK) schemes are popular high order time discretization methods for solving stiff kinetic equations. As opposed to the compressible Euler limit (leading order asymptotics of the Boltzmann equation as the Knudsen number \(\varepsilon \) go...
作者:Xiangxiong Zhang
来源:[J].Journal of Computational Physics(IF 2.138), 2017, Vol.328, pp.301-343
摘要:Abstract(#br)We construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–Stokes equations, which can be easily extended to multiple dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-pre...
作者:Sashank Srinivasan , Jonathan Poggie , Xiangxiong Zhang
来源:[J].Journal of Computational Physics(IF 2.138), 2018, Vol.366, pp.120-143
摘要:Abstract(#br)For constructing high order accurate positivity-preserving schemes for convection–diffusion equations, we construct a simple positivity-preserving diffusion flux. Discontinuous Galerkin (DG) schemes with such a positivity-preserving diffusion flux are nonlinear ...
作者:Xiangxiong Zhang
来源:[J].Journal of Computational Physics(IF 2.138), 2016, Vol.308, pp.153-170
摘要:Abstract(#br)For problems defined in a two-dimensional domain Ω with boundary conditions specified on a curve Γ, we consider discontinuous Galerkin (DG) schemes with high order polynomial basis functions on a geometry fitting triangular mesh. It is well known that directly i...
作者:Xiangxiong Zhang , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2009, Vol.229 (9), pp.3091-3120
摘要:Abstract(#br)We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillat...
作者:Xiangxiong Zhang , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2010, Vol.229 (23), pp.8918-8934
摘要:Abstract(#br)We construct uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for Euler equations of compressible gas dynamics. The same framework also applies to high order accurate finite volume (e.g. essentially n...
作者:Xiangxiong Zhang , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2011, Vol.230 (4), pp.1238-1248
摘要:Abstract(#br)In [16,17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies t...
作者:Xiangxiong Zhang , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2011, Vol.231 (5), pp.2245-2258
摘要:Abstract(#br)In Zhang and Shu (2010)[20], Zhang and Shu (2011)[21] and Zhang et al. (in press)[23], we constructed uniformly high order accurate discontinuous Galerkin (DG) and finite volume schemes which preserve positivity of density and pressure for the Euler equations of comp...
作者:Yifan Zhang , Xiangxiong Zhang , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2013, Vol.234, pp.295-316
摘要:Abstract(#br)We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a strict maximum principle for general nonlinear convection–diffusion equations on unstructured triangular meshes. Motivated by genuinely high order maximum-principle-satisfying D...
作者:Xiangxiong Zhang , Chi-Wang Shu
来源:[J].Journal of Computational Physics(IF 2.138), 2011, Vol.231 (2), pp.653-665
摘要:Abstract(#br)One of the main challenges in computational simulations of gas detonation propagation is that negative density or negative pressure may emerge during the time evolution, which will cause blow-ups. Therefore, schemes with provable positivity-preserving of density...

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