In strong-form methods, nonphysical oscillation occurs when the flow problem is simulated on a nonstaggered grid. The purpose of this paper is to apply a strong-form method, finite line method (FLM), to simulate incompressible flow and heat transfer problems.
The FLM is a kind of strong-form numerical method that combines the superiority of the meshless method in terms of geometric adaptability and the finite difference method in terms of ease of use. The FLM can easily construct higher-order scheme because the recursion principle is used to compute higher-order spatial derivatives. In addition, the authors present the upwind scheme FLM to deal with the unphysical oscillation, and five numerical examples are calculated to prove the correctness of FLM.
In the FLM, increasing the number of nodes in each line-set and adopting the upwind scheme can demonstrate their efficacy in improving numerical results of unphysical oscillation. And both the FLM and the upwind scheme FLM can obtain very accurate results. For example, the L2-norm error can be as small as 10–12 when solving the Kovasznay flow problem.
To the best of the authors’ knowledge, this paper is the first to apply the FLM to solve fluid flow and heat transfer problems. This enhances the application value of the FLM in the numerical simulation of multifield coupling problems for engineering applications. Moreover, the authors effectively solved the nonphysical oscillation, which can provide a reference for other strong-form algorithms to solve this problem on nonstaggered grids.
