Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

转动坐标系中三维跨声速欧拉流的有限体积-TVD格式

在非惯性转动坐标系中,本文采用贴体网格、有限体积法离散和修正数值通量技术,将Harten的一维TVD格式推广到三维。由于转动使方程出现源项,文中通过对源项的巧妙处理,使修改后的格式能用于非齐次双曲守恒律方程组高分辨率的数值计算。为了加速解的收敛,提高显式时间推进的CFL数,本文采用隐式残值光顺技术。三维跨声速带非齐次源项欧拉方程的典型算例表明:捕捉的激波分辨率较高;激波前后没有发现大的数值波动和伪振荡现象;所得的跨声速流场解与实验较接近。

PB 18 TVD

Dark brown sediment with organic material present throughout. The clasts are mainly small. Lineations are abundant throughout the sample.

TvD PB #61

Brown sediment with well dispersed clasts ranging from small to large. Clast shape ranges from angular to sub-rounded. Lineations can be seen throughout the sample. There is one small patch of another domain present. This domain is light brown, and contains clasts that are clustered together. Grain crushing is abundant in this domain, as well as in other areas of the sample.

TVD #9 PB

Dark brown sediment (almost black), with a few clasts that are very well dispersed. The clasts range from small to medium in size. The clast shape ranges from sub-angular to rounded. The sample is mainly structureless. There are a few inclusions of a lighter domain. This domain contains more clasts than the darker one.

WTS-1-TvD

Brown sample with two mains domains. The general clast shape ranges from sub-angular to sub-rounded. The first one is light brown with closely clustered clasts ranging from small to large. Lineations are common amongst the smaller clasts. Grain crushing is commonly seen with larger clasts. The other domain is a darker brown with better dispersed clasts ranging from small to medium. Lineations are common in this domain.

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.