A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum, and energy equations are solved by different methods. It especially designed here developing new discretizations of the total equation adapted a thermal coupling with lattice Boltzmann method (LBM). The proposed linear equivalence standard entropy e...

High order fast sweeping methods have been developed recently in the literature to solve static Hamilton-Jacobi equations efficiently. Comparing with the first order fast sweeping methods, the high order fast sweeping methods are more accurate, but they often require additional numerical boundary treatment for several grid points near the boundary because of the wider numerical stencil. It is p...

To gain insight into cardio-arterial interactions, a coupled left ventricle-systemic artery (LV-SA) model is developed that incorporates a three-dimensional finite-strain left ventricle (LV), and a physiologically-based one-dimensional model for the systemic arteries (SA). The coupling of the LV model and the SA model is achieved by matching the pressure and the flow rate at the aortic root, i....

Abstract A quasi–second-order scheme is developed to obtain approximate solutions of the two-dimensional shallow water equations (SWEs) with bathymetry. The based on a staggered finite volume space discretization: scalar unknowns are located in discretization cells while vector edges mesh. monotonic upwind-central for conservation laws (MUSCL)-like interpolation discrete convection operators he...

The Lax-Friedrichs (LxF) method [2, 3, 4] is a basic method for the solution of hyperbolic partial differential equations (PDEs). Its use is limited because its order is only one, but it is easy to program, applicable to general PDEs, and has good qualitative properties because it is monotone. The LxF method is often used to show the effects of dissipation, but it is not actually a dissipative ...

The Lax-Richtmyer theorem is extended to work in the framework of Stetter's theory of discretizations. The new result applies to both initial and boundary value problems discretized by finite elements, finite differences, etc. Several examples are given, together with a comparison with other available equivalence theorems. The proof relies on a generalized Banach-Steinhaus theorem.