Numerical solutions presented in a companion paper show that two-dimensional mesoscale terrain becomes a much stronger barrier to a continuously stratified flow when the flow contains warm advection. Here it is shown that this baroclinic enhancement is a strictly nonlinear phenomenon. The linear analysis indicates a weakening of the upstream response in warm advection. However, a weakly nonline...

In this paper, we propose a new conservative hybrid finite element-finite difference method for the Vlasov equation. The proposed methodology uses Strang splitting to decouple the nonlinear high dimensional Vlasov equation into two lower dimensional equations, which describe spatial advection and velocity acceleration/deceleration processes respectively. We then propose to use a semi-Lagrangian...

In a numerical, isopycnal, ocean model the mixing is investigated with the environment of two idealized Agulhas rings, one that splits, and one that remains coherent. The evolution of a passive tracer, initially contained within the rings, shows that tracer leakage is associated with the formation of filaments in the early stage of ring evolution. These filaments reach down to the thermocline. ...

We describe a multigrid method for solving the steady Euler equations in O(N) operations, where N is the number of unknowns, based on an elliptic/hyperbolic decomposition achieved by local preconditioning. The splitting allows the embedded advection equations to be treated with streamwise semicoarsening rather than full coarsening, which would not be effective. A simple 2-D numerical computatio...

The aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems arising from the discontinuous Galerkin method. The smoothed aggregation multigrid, introduced by Vaněk for the conforming finite element method, is applied to low-order discretizations of convection-diffusion equations. For the elliptic model ...

A method for solving the saturation equation for two-phase ow is presented. The method may be viewed as an operator splitting method or as an Eulerian-Lagrangian backtracking procedure or as a modiied method of characteristics. For each time step, the method consists of an advection step and a diiusion step. The advection step requires the tracking of streamlines locally around certain integrat...

An efficient method for scalar advection is developed that selectively preserves monotonicity. Monotonicity preservation is applied only where the scalar field is likely to contain discontinuities as indicated by significant grid-cell-to-grid-cell variations in a smoothness measure conceptually similar to that used in weighted essentially non-oscillatory (WENO) methods. In smooth regions, the n...

this paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the accelerated overrelaxation (aor) method. in this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

A numerical scheme, upstream biased Eulerian algorithm for transport equations with sources (UpBEATES), is developed for solving a scalar advective-dominated transport equation with concentration-independent and -dependent source terms. A controlvolume method is used for spatial discretization. Time integration is invoked to yield a discrete system of integrated-flux-integratedsource form equat...

A numerical model is presented for computation of unsteady two-fluid interfaces in nonlinear porous media flow. The nonlinear Forchheimer equation is included in the Navier-Stokes equations for porous media flow. The model is based on capturing the interface on a fixed mesh domain. The zero level set of a pseudo-concentration function, which defines the interface between the two fluids, is gove...