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Abstract
The sharp and high-order treatment of arbitrary boundaries immersed in the computational domain remains a challenge to particle methods. While several techniques have been proposed to modify numerical stencils, e.g. Finite Difference ones, near the walls, the particle–mesh interpolation component of particle methods also has to be modified. This operation, mapping fields from the grid to the particles and vice-versa, has to be performed several times per computational step in the framework of particle–mesh methods. The present paper proposes an extension of classical particle–mesh interpolation approaches by computing high-order ghost fields based on the information about the solution behavior at the wall. This approach is further shown to be especially interesting when combined with a dimension-splitting Immersed Interface method to correct the spatial differential operators. Indeed, the associated corrections are computed at the intersection between the interface and the grid lines, making the necessary information for the ghost construction readily available. The mesh-to-particles and particles-to-mesh interpolation schemes are validated individually in convergence studies and, finally, both are applied to the advection–diffusion of a passive tracer past 2D objects.
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Marichal, Y., Chatelain, P., & Winckelmans, G. (2016). Immersed interface interpolation schemes for particle–mesh methods. Journal of Computational Physics, 326(1), 947-972. https://doi.org/10.1016/j.jcp.2016.09.027 (Original work published 2016)