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231225s2018 xx |||||o 00| ||eng c |
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|a 10.1016/j.jcp.2018.06.036
|2 doi
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|a eng
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|a Shankar, Varun
|e verfasserin
|4 aut
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|a Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations
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|c 2018
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|a Text
|b txt
|2 rdacontent
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|a ƒaComputermedien
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|2 rdamedia
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|a ƒa Online-Ressource
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|a Date Revised 11.10.2023
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|a published: Print-Electronic
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|a Citation Status PubMed-not-MEDLINE
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|a We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advectiondiffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and implicit-explicit (IMEX) time integrators by using a simple 1D semi-discrete Von Neumann analysis. The analysis is applied to an analytical model of spurious growth in RBF-FD solutions that uses auxiliary differential operators mimicking the undesirable properties of RBF-FD differentiation matrices. The resulting hyperviscosity formulation is a generalization of existing ones in the literature, but is free of any tuning parameters and can be computed efficiently. To further improve robustness, we introduce a simple new scaling law for polynomial-augmented RBF-FD that relates the degree of polyharmonic spline (PHS) RBFs to the degree of the appended polynomial. When used in a novel ghost node formulation in conjunction with the recently-developed overlapped RBF-FD method, the resulting method is robust and free of stagnation errors. We validate the high-order convergence rates of our method on 2D and 3D test cases over a wide range of Peclet numbers (1-1000). We then use our method to solve a 3D coupled problem motivated by models of platelet aggregation and coagulation, again demonstrating high-order convergence rates
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|a Journal Article
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|a Radial basis function
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|a advection-diffusion
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|a high-order method
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| 650 |
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|a hyperviscosity
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| 650 |
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|a meshfree
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| 700 |
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|a Fogelson, Aaron L
|e verfasserin
|4 aut
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| 773 |
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|i Enthalten in
|t Journal of computational physics
|d 1986
|g 372(2018) vom: 01. Nov., Seite 616-639
|w (DE-627)NLM098188844
|x 0021-9991
|7 nnas
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| 773 |
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|g volume:372
|g year:2018
|g day:01
|g month:11
|g pages:616-639
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|u http://dx.doi.org/10.1016/j.jcp.2018.06.036
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