An efficient low‐dissipative WENO filter scheme

This paper presents a simple and efficient procedure developed for tracing discontinuities in flow fields. Numerical experiments are carried out to test the new sensor coupled with the associated nonlinear WENO dissipation filter developed to suppress the numerical dissipation. The tests show that, for a problem containing shocks and vortices, the implementation of the new sensor and an optimized WENO scheme can obtain a stable and highly resolved solution. The numerical experiments demonstrated that the new filter scheme performs efficiently both in parallel and serial running for one‐dimensional inviscid flow problems. Direct numerical simulation of a Mach 5 turbulent boundary layer over a flat plate was carried out to demonstrate the applicability of the scheme to the DNS practices. Copyright © 2011 John Wiley & Sons, Ltd.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).     

A note on compressive limiting for two‐material flows

In this short note we describe a simple extension to the multi‐material shock‐capturing algorithm presented in (J. Comput. Phys. 2007; 223 :262–297) that can be used to maintain sharp material interfaces. The method takes the form of an artificial compression which is designed so that the material indicator jumps across only a few cells but which does not excite physical instabilities in the flow. The advantages of the approach include its simplicity and flexibility in that it provides a parameter that effectively determines the captured interface thickness. Copyright © 2009 John Wiley & Sons, Ltd.     

A blow‐up criterion to the 2D full compressible magnetohydrodynamic equations

We establish a new regularity criterion for the 2D full compressible magnetohydrodynamic system in a bounded domain. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence of global weak solutions for Navier‐Stokes‐Poisson equations with quantum effect and convergence to incompressible Navier‐Stokes equations

In this paper, we consider a three dimensional quantum Navier‐Stokes‐Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier‐Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

统一的对流扩散型可压缩流体力学方程与解法

流体力学的动量方程、能量方程、湍动能方程和耗散方程都具有对流扩散方程的形式,但连续方程却不是对流扩散型的。对于可压缩问题,本文通过合理的数学推导,不作任何近似、假定与简化,得到一个全新的连续方程形式．该连续方程以压力为未知变量,并具有对流扩散型形式,使得所有的流体动力学方程组都具有完全统一的方程形式,给出了这种三维对流扩散方程组的有限精确差分计算格式。对流体力学的进一步发展具有一定意义．     

热声波数值模拟的虚假振荡研究

采用可压缩流动的SIMPLE算法对一维封闭空腔内由边界突然加热所引起的非稳态热声波进行了数值模拟,对流-扩散项采用了中心差分、一阶迎风差分、QUICK、及MIJSCL等不同格式。计算表明各种格式均存在不同程度的虚假振荡现象,其大小与热声波的强度及离散格式的形式等多种因素有关。这些结果对热声波的进一步研究及高效可靠的对流差分格式的开发具有重要意义。     

Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier–Stokes: Applications to fluid–structure interaction

Stabilised mixed velocity–pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier–Stokes. In these formulations, the Newton–Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton–Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed finite element formulation for incompressible Navier–Stokes that preserves second-order temporal accuracy of the generalised-alpha and related schemes for both velocity and pressure fields. First, we demonstrate the second-order temporal accuracy using numerical convergence studies for an example with a manufactured solution. Later, we assess the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder. Towards showcasing the applicability of the proposed technique in a wider context, the inf–sup stable P2–P1 pair for the formulation without stabilisation is also considered. Finally, the resulting benefits of using the proposed scheme for fluid–structure interaction problems are illustrated using two benchmark examples in fluid-flexible structure interaction.     

A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.