Lattice Boltzmann flux solver for simulation of hypersonic flows

In this paper, a stable Lattice Boltzmann Flux Solver (LBFS) is proposed for simulation of hypersonic flows. In LBFS, the finite volume method is applied to solve the Navier-Stokes equations. One-dimensional Lattice Boltzmann model is applied to reconstruct the inviscid flux across the cell interface, while the viscous flux is solved by conventional smooth approximation function. The present work extends the existing LBFS to calculate hypersonic flow field on the leeward, which is hard to get convergent results due to extremely low pressure effects in this area. Simulation of a biconics model is studied. It is discovered that the tail area of double cone is related to the maximum Mach number that could be convergent. The larger the diameter of tail area is, the smaller Mach number could be convergent. Hence, the low pressure area behind double cone tail will have large effects during the LBFS simulation of hypersonic flow. Two measurements are applied in this paper to overcome the low pressure problem. The first one is to apply a local block grid refinement method based on the flow conditions for improving the stability. The second is to add a constraint parameter to eliminate negative value and give out a proper one. Hence, LBFS is able to get convergent result of the hypersonic flow field on both windward and leeward. Several numerical examples are tested to compare the performance of method presented in this paper. Simulation results show that method present in this paper is able to calculate hypersonic flow field on the leeward with both fine accurate and efficient

A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows

10.1016/j.jcp.2015.03.058Journal of Computational Physics295322-33

DEVELOPMENT OF GAS KINETIC FLUX SOLVERS AND THEIR APPLICATIONS

Ph.DDOCTOR OF PHILOSOPH

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time