We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in t...

In this work, a first-order upwind and a high-order flux-limiter schemes for solving the advection–diffusion equation on unstructured grids were evaluated. The numerical schemes were implemented as a module of an unstructured two-dimensional depth-averaged circulation model for shallow lakes (IPH-UnTRIM2D), and they were applied to the Guaíba River in Brazil. Their performances were evaluated b...

Central schemes offer a simple and versatile approach for computing approximate solutions of non-linear systems of hyperbolic conservation laws and related PDEs. The solution of such problems often involves the spontaneous evolution of steep gradients. The multiscale aspect of these gradients poses a main computational challenge for their numerical solution. Central schemes utilize a minimal am...

A kinetic flux-vector splitting (KFVS) scheme is applied for solving a reduced six-equation two-phase flow model of Saurel et al. [1]. The model incorporates single velocity, two pressures and relaxation terms. An additional seventh equation, describing the total mixture energy, is added to the model to guarantee the correct treatment of shocks in the single phase limit. Some salient features o...

In this paper, we review and construct fifthand ninth-order central weighted essentially nonoscillatory (WENO) schemes based on a finite volume formulation, staggered mesh, and continuous extension of Runge–Kutta methods for solving nonlinear hyperbolic conservation law systems. Negative linear weights appear in such a formulation and they are treated using the technique recently introduced by ...

in this paper, a viscous flow simulation is presented using the lattice boltzmann equation (lbe). a finite volume approach is adapted to discretize the lbe on a cell-centered, arbitrary shaped, rectangular tessellation. the formulation includes upwind scheme and high order descretization schemes for the flux term and collision operator respectively. a consistent open and solid boundary treatmen...

Uniform convergence analysis of an upwind nite-diierence approximation of a convection-diiusion boundary value problem on an adaptive grid. We derive an-uniform error estimate for the rst-order upwind discretisation of a model convection-diiusion boundary value problem on a non-uniform grid. Here, is the small parameter multiplying the highest derivative term. The grid is suggested by the equid...