2019/01/24 by Shirzad Hosseinverdi, Hosseinverdi, Shirzad, Hermann F. Fasel +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1901.08269
openalex publication_date 2019/01/24 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
This paper presents an efficient high-order sharp-interface method for\nsolving the three-dimensional (3D) Poisson equation with Dirichlet boundary\nconditions on a nonuniform Cartesian grid with irregular domain boundaries. The\nnew approach is based on the combination of the fourth-order compact finite\ndifference scheme and the preconditioned stabilized biconjugate-gradient\n(BiCGSTAB) method. Contrary to the original immersed interface method by\nLeVeque and Li [1], the new method does not require jump corrections, instead,\nthe (regular) compact finite difference stencil is adjusted at the irregular\ngrid points (in the vicinity of the interfaces of the immersed bodies) to\nobtain a solution that is sharp across the interface while keeping the\nfourth-order global accuracy. The contribution of the present work is the\ndesign of a fourth-order-accurate 3D Poisson solver whose accuracy and\nefficiency does not deteriorate in the presence of an immersed boundary. This\nis attributed to (i) the modification of the discrete operators near immersed\nboundaries does not lead to a wide grid stencil due to the compact nature of\nthe discretization and (ii) a preconditioning technique whose efficiency and\ncost are independent of the complexity of the geometry and the presence or not\nof an immersed boundary. The accuracy and computational efficiency of the\nproposed algorithm is demonstrated and validated over a range of problems\nincluding smooth and irregular boundaries. The test cases show that the new\nmethod is fourth-order accurate in the maximum norm whether an immersed\nboundary is present or not, on uniform or nonuniform grids. Furthermore, the\nefficiency of the preconditioned BiCGSTAB is demonstrated with regard to\nconvergence rate and `extra' floating-point operation (FLOPextra) which is\ndue to the presence of immersed boundaries.\n