An efficient ghost fluid method for compressible multifluids in Lagrangian coordinate

In this paper, we present an extended ghost fluid method (GFM) for computations of inviscid compressible multifluids in Lagrangian coordinate. That is, we capture the appropriate interface conditions by defining a fluid that has the velocity and the pressure of the real fluid at each point, but the entropy or the internal energy of some other fluid. Meanwhile, a single-fluid solver, CWENO-type central-upwind scheme, is developed in Lagrangian coordinate. The high resolution and the non-oscillatory quality of the scheme can be verified by solving several numerical experiments.     

EXISTENCE AND UNIQUENESS RESULTS FOR VISCOUS, HEAT-CONDUCTING 3-D FLUID WITH VACUUM

We prove the local existence and uniqueness of the strong solution to the 3-D full Navier-Stokes equations whose the viscosity coefficients and the thermal conductivity coefficient depend on the density and the temperature. The initial density may vanish in an open set and the domain could be bounded or unbounded. Finally, we show the blow-up of the smooth solution to the compressible Navier-Stokes equations in R^n （n 〉 1） when the initial density has compactly support and the initial total momentum is nonzero.     

Evaluation of adaptive mesh refinement and coarsening for the computation of compressible flows on unstructured meshes

The compressible gas flows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed flows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh finite volume upwind computer code. This scheme is tailored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

A high‐order element‐based Galerkin method for the barotropic vorticity equation

A high‐order element‐based Galerkin method is developed to solve the non‐divergent barotropic vorticity equation (BVE). The solution process involves solving a conservative transport equation for the vorticity fields and a Poisson equation for the stream function fields. The discontinuous Galerkin method is employed for solving the transport equation and a spectral element method (continuous Galerkin) is used for the Poisson equation. A third‐order strong stability preserving explicit Runge–Kutta scheme is used for time integration. A series of tests have been performed to validate the model, which include the evolution of an idealized tropical cyclone and interaction of dual vortices in close proximity. The numerical convergence study is performed by solving the BVE on the sphere where the analytic solution is known. The test results are consistent with physical observations, and the model exhibits exponential convergence. Copyright © 2008 John Wiley & Sons, Ltd.     

A lattice Boltzmann model for the compressible Euler equations with second‐order accuracy

In this paper, we propose a new lattice Boltzmann model for the compressible Euler equations. The model is based on a three‐energy‐level and three‐speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. In order to obtain second‐order accuracy, we employ the ghost field distribution functions to remove the non‐physical viscous parts. We also use the conditions of the higher moment of the ghost field equilibrium distribution functions to obtain the equilibrium distribution functions. In the numerical examples, we compare the numerical results of this scheme with those obtained by other lattice Boltzmann models for the compressible Euler equations. Copyright © 2008 John Wiley & Sons, Ltd.     

Specific heat ratio effects of compressible Rayleigh–Taylor instability studied by discrete Boltzmann method

Rayleigh–Taylor (RT) instability widely exists in nature and engineering fields. How to better understand the physical mechanism of RT instability is of great theoretical significance and practical value. At present, abundant results of RT instability have been obtained by traditional macroscopic methods. However, research on the thermodynamic non-equilibrium (TNE) effects in the process of system evolution is relatively scarce. In this paper, the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT instability. The evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium region. Firstly, as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region, the average TNE intensity first increases and then reduces, and it increases with the specific heat ratio decreasing; the specific heat ratio has the same effect on the global strength of the viscous stress tensor. Secondly, the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex structure. Thirdly, under the competition between the temperature gradients and the contact area of the two fluids, the average intensity of the non-equilibrium quantity related to the heat flux shows diversity, and the influence of the specific heat ratio is also quite remarkable.     

Efficient implicit algorithm for the equations of 2-D viscous compressible flow: application to shock-boundary layer interaction

A fully implicit algorithm has been developed to time integrate the equations of 2-D compressible viscous flow. The algorithm was constructed so as to optimize computational efficiency. The time-consuming block matrix inversions usually associated with implicit algorithms have been reduced to the trivial non-iterative inversion of four sets of scalar bidiagonal matrices. Thus, the algorithm requires virtually no more computer storage than an explicit algorithm. The efficient structure of the implicit algorithm is reflected in comparative timings which slow that it requires only a factor of two more computer time per point per time step than a typical explicit algorithm. Therefore, the algorithm allows more economical solution of given flows than existing explicit methods and also allows more difficult problems to be attempted using available computer resources. Application of the algorithm to the problem of shock-boundary layer interaction produces results consistent with both experimental measurements and other calculations.     

幂硬化可压缩材料Ⅰ型动态裂纹尖端奇异场

研究了平面应变条件下幂硬化可压缩材料中定常扩展的Ⅰ型动态裂纹尖端应力应变奇异场．采用Ｊ２流动理论和场量直角坐标分量，得到了应力应变奇异性不同时的裂纹尖端渐近场，其中场量的角变化规律和理想弹塑性材料的完全相同