The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which m...

The e ect of arti cial di usion on discrete shock structures is examined for a family of schemes which includes scalar di usion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristic splitting. The analysis leads to conditions on the di usive ux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets th...

In this paper, we present consistent and inconsistent discontinuous Galerkin methods for incompressible Euler Navier-Stokes equations with the kinematic pressure, Bernoulli function EMAC function. Semi- fully discrete energy stability of proposed dG are proved in a unified fashion. Conservation total energy, linear angular momentum is discussed both central upwind fluxes. Numerical experiments ...

We consider the numerical approximation of the shallow–water equations with non–flat topography. We introduce a new topography discretization that makes all schemes to be well–balanced and robust. At the discrepancy with the well–known hydrostatic reconstruction, the proposed numerical procedure does not involve any cut–off. Moreover, the obtained scheme is able to deal with dry areas. Several ...

In this paper, we present an upwinding methodology for systems of conservation laws. Our aim is to construct upwind schemes which do not require the extraction of the eigensystem of the jacobian matrix (but just the knowledge of the eigenvalues) and rely on the introduction of an appropriate polynomial approximation. @U @t + @F(U) @x = 0; t > 0; x 2 I R ; (1) avec U(x; t) un etat de l'espace de...

The constrained transport (CT) method reflects the state of art numerical technique for preserving divergence-free condition magnetic field to machine accuracy in multi-dimensional MHD simulations performed with Godunov-type, or upwind, conservative codes. evolution different components, located at zone interfaces using a staggered representation, is achieved by calculating electric components ...

In this paper we present a general framework for designing an analyzing high order in time fractional step schemes for integrating evolutionary convection-diffusion-reaction multidimensional problems. These methods are deduced, for example, by combining standard semidiscretization techniques (upwind) and a special kind of Runge-Kutta type schemes called Fractionary Steps Runge-Kutta methods. We...