The algebraic immersed interface and boundary method for elliptic equations with jump conditions

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 to impose 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. Corresponding author: [email protected] 0AMS Classification: 65N06, 65Y20 1 ONERA The French Aerospace Lab, BP 74025, 2 avenue Edouard Belin, 31055 Toulouse Cedex 4, France 2Université de Bordeaux, Institut de M ́ecanique et Ing ́enierie (I2M) UMR 5295, F-33400 Talence, France 3Université de Provence, Laboratoire LATP-CMI, UMR-CNRS 6632, Technopôle Château-Gombert, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France 1 ha l-0 03 90 07 5, v er si on 3 8 M ay 2 01 2