The odd-even hopscotch pressure correction scheme for the incompressible Navier-Stokes equations

AbstractThe odd-even hopscotch (OEH) scheme, which is a time-integration technique for time-dependent partial differential equations, is applied to the incompressible Navier-Stokes equations in conservative form. In order to decouple the computation of the velocity and the pressure, the OEH scheme is combined with the pressure correction technique. The resulting scheme is referred to as the odd-even hopscotch pressure correction (OEH-PC) scheme. As a numerical example, we use the OEH-PC scheme to compute the flow through a reservoir. This contribution is based on the work reported in [13]. We refer to that paper for a more comprehensive discussion of the OEH-PC scheme

The complete flux scheme in cylindrical coordinates

We consider the complete ¿ux (CF) scheme, a ¿nite volume method (FVM) presented in [1]. CF is based on an integral representation for the ¿uxes, found by solving a local boundary value problem that includes the source term. It performs well (second order accuracy) for both diffusion and advection dominated problems. In this paper we focus on cylindrically symmetric conservation laws of advection-diffusion-reaction type. [1] ten Thije Boonkkamp, J.H.M., Anthonissen, M.J.H.: The ¿nite volume-complete ¿ux scheme for advection-diffusion-reaction equations. Journal of Scienti¿c Computing 46(1), 47–70 (2011

The finite volume-complete flux scheme for one-dimensional advection-diffusion-reaction equations

We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme, which is second order accurate, uniformly in the local Peclet numbers. The flux approximation is combined with a finite volume method, and the resulting finite volume-complete flux scheme is validated for several test problems

An exponential fitting scheme for the electrothermal device equations, specifically for the simulation of avalanche generation

An extension of the Scharfetter-Gummel discretization scheme is presented which is designed for electrothermal semiconductor device equations including avalanche generation terms. The scheme makes explicit use of the exponential character of solutions, and reduces to the standard Scharfetter-Gummel scheme in the isotherma