A Correction Function-based KFBI Method for Brinkman Interface Problems
It provides a novel numerical method for solving interface problems with discontinuous coefficients in fluid dynamics, offering improved accuracy over existing methods.
The paper proposes a correction-function-based kernel-free boundary integral method for Stokes- and Brinkman-type interface problems, achieving high accuracy and efficiency in numerical experiments with both fixed and moving interfaces.
In this work, we propose a correction-function-based kernel-free boundary integral (CF-KFBI) method for solving Stokes- and Brinkman-type interface problems. We begin by recasting the original interface problem with discontinuous coefficients as boundary integral equations, in which the integral operators can be interpreted as boundary data for potential functions that satisfy simpler interface problems without coefficient discontinuities. Each such interface problem is discretized using a corrected Marker-and-Cell (MAC) scheme. Within a narrow band around the interface, we introduce a local correction function that represents the solution jump, leading to a local Cauchy problem. This problem is solved with a collocation method, for which we provide criteria for a minimal choice of collocation points and prove solvability. Several numerical experiments, including both fixed- and moving-interface problems, are presented to demonstrate the accuracy and efficiency of the proposed method.