We construct the cell-centered Finite Volume discretization of the twodimensional inviscid primitive equations in a domain with topography. To compute the numerical fluxes, the so-called Upwind Scheme (US) and the Central-Upwind Scheme (CUS) are introduced. For the time discretization, we use the classical 4th order RungeKutta method. We verify, with our numerical simulations, that the US (or C...

A unified theory of non-oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated ...

We analyze the convergence of the multiplicative Schwarz method applied to nonsymmetric linear algebraic systems obtained from discretizations of one-dimensional singularly perturbed convection-diffusion equations by upwind and central finite differences on a Shishkin mesh. Using the algebraic structure of the Schwarz iteration matrices we derive bounds on the infinity norm of the error that ar...

Two time-splitting methods for integrating the elastic equations are presented. The methods are based on a third-order Runge–Kutta time scheme and the Crowley advection schemes. The schemes are combined with a forward–backward scheme for integrating high-frequency acoustic and gravity modes to create stable splitexplicit schemes for integrating the compressible Navier–Stokes equations. The time...

Abstract. We consider the use of finite volume methods for the approximation of a parabolic variational inequality arising in financial mathematics. We show, under some regularity conditions, the convergence of the upwind implicit finite volume scheme to a weak solution of the variational inequality in a bounded domain. Some results, obtained in comparison with other methods on two dimensional ...

Finite Volume Methods (FVM) are high quality methods for solving conservative/hyperbolic partial differential equations (PDEs). A popular class of high-resolution utilize a nonlinear combination low order and via flux limiting functions. Another is the weighted essentially non-oscillatory (WENO) schemes. Here, focus on An experimental finite volume (FV) semi-discrete solver systems hyperbolic P...