A high-order immersed interface method free of derivative jump conditions for Poisson equations on irregular domains

Autor(es)

Colnago, Marilaine ^[1] ; Casaca, Wallace ^[2] ; de Souza, Leandro Franco ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Av Trabalhador Sao Carlense 400, Sao Carlos - Brazil

^[2] Univ Estadual Paulista UNESP, Dept Engn Energia, Av Barrageiros 1881, Rosana - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Computational Physics; v. 423, DEC 15 2020.
• Citações Web of Science: 0

Resumo

Immersed Interface Methods (IIM) arise as a very effective tool to solve many interface problems encountered in fluid dynamics, mechanics and other related fields of study. Despite their versatility and potential, IIM-inspired techniques impose as constraints different types of jump conditions in order to be mathematically tractable and usable in practice. To cope with this issue, in this paper we introduce a novel Immersed Interface method for solving Poisson equations with discontinuous coefficients on Cartesian grids. Different from most conventional methods which assume some derivative information at the interface to produce a valid approximation, our approach reduces the number of regular constraints when solving the Poisson problem, requiring to be given only the ordinary jumps of the function. We combine Finite Difference schemes, ghost node strategy, correction formulas, and interpolation rules into a unified and stable numerical model. Moreover, the present method is capable of producing high-order solutions from a unique resource of available data. We attest to the accuracy and robustness of our single jumpbased method through a variety of numerical experiments comprising Poisson problems with interfaces that can be now solved from a reduced number of jump conditions. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs