The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions
Idioma
en
Article de revue
Este ítem está publicado en
Open Journal of fluid Dynamics. 2020, vol. 10, n° 3, p. 239 - 269
Scientific Research
Resumen en inglés
A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed ...Leer más >
A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance , the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.< Leer menos
Palabras clave en inglés
Fictitious Domain
Immersed Interface Method
Immersed Boundary Method
Penalty Methods
Finite Volumes
Elliptic Equations
Jump Embedded Conditions
Orígen
Importado de HalCentros de investigación