A Seamless, Extended DG Approach for Advection–Diffusion Problems on Unbounded Domains
| Autor: | Luca Bonaventura, Federico Vismara, Tommaso Benacchio |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Numerical Analysis
010504 meteorology & atmospheric sciences Discretization Basis (linear algebra) Applied Mathematics General Engineering Basis function 010103 numerical & computational mathematics 01 natural sciences Domain (mathematical analysis) Theoretical Computer Science Computational Mathematics Polynomial basis Computational Theory and Mathematics Discontinuous Galerkin method Laguerre polynomials Applied mathematics Boundary value problem 0101 mathematics Software 0105 earth and related environmental sciences Mathematics |
| Zdroj: | Journal of Scientific Computing |
| Popis: | We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection–diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test functions. Numerical fluxes enable the coupling at the interface between the two subdomains in the same way as standard single domain DG interelement fluxes. A novel linear analysis on the extended DG model yields unconditional stability with respect to the Peclet number. Errors due to the use of different sets of basis functions on different portions of the domain are negligible, as highlighted in numerical experiments with the linear advection–diffusion and viscous Burgers’ equations. With an added damping term on the semi-infinite subdomain, the extended framework is able to efficiently simulate absorbing boundary conditions without additional conditions at the interface. A few modes in the semi-infinite subdomain are found to suffice to deal with outgoing single wave and wave train signals more accurately than standard approaches at a given computational cost, thus providing an appealing model for fluid flow simulations in unbounded regions. |
| Databáze: | OpenAIRE |
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