In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes on two-dimensional unstructured triangular meshes [35], to the correction procedure via reconstruction (CPR) framework for solving nonlinear hyperbolic conservation laws on two-dimensional unstructured triangular meshes with straight edges or curved e...

We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods and apply them to non-conservative semi-Lagrangian schemes and conservative finite difference methods. Our numerical results will be compared to the usual sem...

ENO (essentially nonoscillatory) and weighted ENO (WENO) schemes were designed for high resolution of discontinuities, such as shock waves, while optimized schemes such as the DRP (dispersion–relation–preserving) schemes were optimized for short waves (with respect to the grid spacing 1x , e.g., waves that are 6–81x in wavelength) in the wavenumber space. In this paper, we seek to unite the adv...

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, ...

This thesis is concerned with effective and robust numerical schemes for solving steady Euler equations. For solving the nonlinear system resulting from the discretization of the steady Euler equations, we employ a standard Newton method as the outer iterative scheme and a linear multigrid method as the inner iterative scheme with the block lower-upper symmetric Gauss-Seidel iteration as its sm...

In this paper we continue our research on the numerical study of convergence to steady state solutions for a new class of finite volume weighted essentially non-oscillatory (WENO) schemes in [38], from tensor product meshes to triangular meshes. For the case of triangular meshes, this new class of finite volume WENO schemes was designed for time-dependent conservation laws in [37] for the third...

For a nonlinear scalar conservation law in one-space dimension, we develop a locally conservative semi-Lagrangian finite difference scheme based on weighted essentially non-oscillatory reconstructions (SL-WENO). This scheme has the advantages of both WENO and semi-Lagrangian schemes. It is a locally mass conservative finite difference scheme, it is formally high-order accurate in space, it has ...

The weighted-essentially non-oscillatory (WENO) schemes have been used to calculate the shock-embedded compressible fluid flow ([9]). The potential high-fidelity qualities of this approach make it attractive for jet noise simulation. However, in its present form, the WENO procedure has many drawbacks that prevent direct applications to jet noise simulations. In this paper, various WENO procedur...