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

Axisymmetric multiphase lattice Boltzmann method

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [ Phys. Rev. E 47 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed

A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the $hp$-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quasilinear parabolic problems. The a posteriori bounds are derived using the elliptic reconstruction framework, utilizing available a posteriori error bounds for the corresponding steady-state elliptic problem.Comment: 8 pages, conference ENUMATH 200

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