A stabilized meshfree reproducing kernel-based method for convection-diffusion problems. (English) Zbl 1242.76232
Summary: In this paper, we develop a meshfree particle-based method for convection-diffusion problems. Discretization is performed by using piecewise constant kernels. The stabilized scheme is based on a new upwind kernel. We show that accurate and stable scheme can be obtained by using purpose-built kernels. It also shown that under some conditions the classical optimal finite difference scheme can be derived by the new method. Several numerical tests validate the method.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76R99 | Diffusion and convection |
Keywords:
meshfree methods; piecewise constant kernels; stabilization; upwinding; convection; diffusion problems; particle methodsReferences:
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