A Galerkin boundary cover method for viscous fluid flows

Abstract

Abstract A Galerkin boundary cover method (GBCM) is developed for modeling of two-dimensional incompressible viscous fluid flows. In this approach, a combination of the finite cover system employed in the numerical manifold method with the Galerkin approximation of the boundary integral equations is presented. It is applicable to both interior and exterior domains due to its naturally variational formulations. In contrast to the domain-type approach, only the boundary data is required in the newly explained method, makes it suitable for the exterior problems. To increase the solution accuracy without refining the local mesh, different cover functions can be implemented on different covers; thereby, the p-adaptive computations can be carried out conveniently. Further, the boundary conditions are imposed accurately and the system matrices are both symmetric and positive definite. The given numerical examples demonstrate the high accuracy and convergence rates of the proposed methodology by using a few covers.