International Journal for Numerical Methods in Fluids

doi: 10.1002/fld.4626pmid: N/A

No abstract is available for this article.

Liao, Shaokai; Zhang, Yan; Chen, Da

doi: 10.1002/fld.4722pmid: N/A

In this paper, for two‐dimensional unsteady incompressible flow, the Navier‐Stokes equations without convection term are derived by the coordinate transformation along the streamline characteristic. The third‐order Runge‐Kutta method along the streamline is introduced to discrete the alternative Navier‐Stokes equations in time, and spacial discretization is carried out by the Galerkin method, and then, the third‐order accuracy finite element method is obtained. Meanwhile, the streamline velocity is uniformly approximated by initial velocity in each time step in order to reduce update frequency of total element matrix and improve calculation efficiency. Finally, some classic unsteady flow examples are calculated and analyzed by different calculation methods, which further demonstrate that the present method has more advantages in stability, permissible time step, dissipation, computational cost, and accuracy. The code can be downloaded at https://doi.org/10.13140/RG.2.2.27706.44484.

Peng, Gang; Gao, Zhiming; Feng, Xinlong

doi: 10.1002/fld.4725pmid: N/A

In this paper, a stabilized extremum‐preserving scheme is introduced for the nonlinear parabolic equation on polygonal meshes. The so‐called harmonic averaging points located at the interface of heterogeneity are employed to define the auxiliary unknowns and can be interpolated by the cell‐centered unknowns. This scheme has only cell‐centered unknowns and possesses a small stencil. A stabilized term is constructed to improve the stability of this scheme. The stability analysis of this scheme is obtained under standard assumptions. Numerical results illustrate that the scheme satisfies the extremum principle with anisotropic full tensor coefficient problems and has optimal convergence rate in space on distorted meshes.

Li, Shaotian; Li, Yineng; Zeng, Zeyu; Huang, Ping; Peng, Shiqiu

doi: 10.1002/fld.4726pmid: N/A

Proper approximation of the force terms, especially the bed slope term, is of crucial importance to simulating shallow water flows in lattice Boltzmann (LB) models. However, there is little discussion on the schemes of adding force terms to LB models for shallow water equations (SWEs). In this study, we evaluate the performance of forcing schemes coupled with different LB models (LABSWE and MLBSWE) in simulating shallow water flows over complex topography and try to find out their intrinsic characteristics and applicability. Three cases are adopted for evaluation, including a stationary case, a one‐dimensional tidal wave flow over an irregular bed, and a steady flow over a two‐dimensional seamount. The simulating results are compared with analytical solutions or the results produced by the finite difference method. For LABSWE, all the forcing schemes, except for the weighting factor method, fail to produce accurate solutions for the test cases; this is probably due to the mismatch between the bed slope term in source terms and the quadratic depth term of the equilibrium distribution functions in these forcing schemes. For MLBSWE, all the forcing schemes are capable of simulating flows over the complex topography accurately; furthermore, those schemes taking into account the collision effect τ to eliminate the momentum induced by forces provide more accurate solutions with quicker convergence as the lattice size decreases. In this view, MLBSWE can bring more flexibility in treating the force terms and thus can be a better tool to simulate shallow water flows over complex topography in practical application.