A family of second order time stepping methods for the Darcy-Brinkman equations

This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing the curvature for velocity, temperature and concentration equations. Accuracy in time is proven and the convergence results for the fully discrete solutions of problem variables are given. Several numerical examples including a convergence study are provided that support the derived theoretical results and demonstrate the efficiency and the accuracy of the method.


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This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, includin...
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Citation Formats
A. Cibik, M. Demir, and S. Kaya Merdan, “A family of second order time stepping methods for the Darcy-Brinkman equations,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 148–175, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34905.