International Journal for Numerical Methods in Fluids

doi: 10.1002/fld.4644pmid: N/A

No abstract is available for this article.

Zeng, Fangjun; Shen, Yiqing; Liu, Shengping; Liu, Li

doi: 10.1002/fld.4747pmid: N/A

Many efforts have been made to improve the accuracy of the conventional weighted essentially nonoscillatory (WENO) scheme at transition points (connecting a smooth region and a discontinuity point). This paper analyzes these works and further develops a more effective multistep WENO scheme. Theoretical analysis and numerical results show that the new scheme not only improves the accuracy by one order higher than the traditional fifth‐order WENO schemes at transition point but also maintains the fifth‐order accuracy in smooth regions even at critical point where the first derivative vanishes.

Kataoka, Takeshi; Hanada, Takaya

doi: 10.1002/fld.4748pmid: N/A

We have developed a fundamentally new type of simple lattice Boltzmann (LB) model for the compressible Navier‐Stokes equations based on the kinetic system proposed by Sone. The model uses the kinetic equation of free‐molecular type in the streaming process and modifies the distribution function to its Chapman‐Enskog type at each time step. Compared with the current LB models, the proposed model is superior in the following two points: (i) there are no inherent errors associated with the Knudsen number; (ii) any flow parameters, including three transport coefficients, can be chosen freely according to our convenience. Numerical tests and error estimates confirm the above statements.

Lin, Xingjian; Wu, Jie; Zhang, Tongwei

doi: 10.1002/fld.4749pmid: N/A

In this paper, a local radial basis function–based semi‐Lagrangian lattice Boltzmann method (RBF‐SL‐LBM) is proposed. This is a mesh‐free method that can be used for the simulation of incompressible flows. In this method, the collision step is performed locally, which is the same as in the standard LBM. In the meanwhile, the steaming step is solved in a semi‐Lagrangian framework. The distribution functions at the departure points, which may be not the grid points in general, are computed by the local radial basis function interpolation. Several numerical tests are conducted to validate the present method, including the lid‐driven cavity flow, the steady and unsteady flow past a circular cylinder, and the flow past an NACA0012 airfoil. The present results are in good agreement with those published in the previous literature, which demonstrates the capability of RBF‐SL‐LBM for the simulation of incompressible flows.