In this paper we further explore and apply our recent anti-diffusive flux corrected high order finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is described by a transport equation. The motivation is that the high order anti-diffusive WENO scheme for conservation laws produces sharp resoluti...

We investigate the applicability of curvilinear grids in the context of astrophysical simulations and WENO schemes. With the non–smooth mapping functions from Calhoun et al. [1], we can tackle many astrophysical problems which were out of scope with the standard grids in numerical astrophysics. We describe the difficulties occurring when implementing curvilinear coordinates into our WENO code, ...

The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. Solutions to hyperbolic conservation laws are often characterized by a large range of length scales as well as discontinuities. Standard nonlinear finite-difference schemes, such as the WENO sche...

In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes [42], to the correction procedure via reconstruction (CPR) framework for solving conservation laws. The objective of this simple WENO limiter is to simultaneously maintain uniform high order accuracy of the CPR framework in smooth regions and control ...

The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. Solutions to hyperbolic conservation laws are often characterized by a large range of length scales as well as discontinuities. Standard nonlinear finite-difference schemes, such as the WENO sche...

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. ...

The two-phase drift flux model is extensively used in multiphase flow applications. In this study, we focus on possible numerical schemes for solving the model. Due to complexity of primitive equations and empirical parameters, it challenging achieve stability scheme high resolution second order central scheme, central-upwind third fifth weighted essentially non-oscillatory (WENO) were successf...

This paper investigates the accuracy and robustness of high order WENO schemes for predicting hypersonic shock wave/boundary layer interaction. The implicit time marching method with unfactored Gauss-Seidel line relaxation is used with a 5th order WENO finite difference scheme for inviscid fluxes. The viscous terms are discretized using a 4th order conservative central differencing. Numerical r...

In this paper we address the problem of producing an enlarged picture from a given digital image. We propose a zooming technique based on ENO and WENO schemes that are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. ENO and WENO schemes have been quite successful in applications, especially for problems containing b...