We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with piecewise smooth solutions containing discontinuities, and have been successful in applications for problems involving both shocks and complicated smooth solution ...

In [19, 20, 22], we constructed uniformly high order accurate discontinuous Galerkin (DG) which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. The technique also applies to high order accurate finite volume schemes. In this paper, we show an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (E...

In this paper, we introduce an improved version of mapped weighted essentially nonoscillatory (WENO) schemes for solving Hamiton-Jacobi equations. To this end, we first discuss new smoothness indicators for WENO construction. Then the new smoothness indicators are combined with the mapping function developed by Henrick et. al. [24]. The proposed scheme yields fifth-order accuracy in smooth regi...

We have proposed a new High Resolution Shock Capturing (HRSC) scheme for Special Relativistic Hydrodynamics (SRHD) based on the semidiscrete central Godunov-type schemes and a modified Weighted Essentially Non-oscillatory (WENO) data reconstruction algorithm. This is the first application of the semidiscrete central schemes with high order WENO data reconstruction to the SRHD equations. This me...

We study WENO(2r-1) reconstruction [Balsara D., Shu C.W.: J. Comp. Phys. 160 (2000) 405–452], with the mapping (WENOM) procedure of the nonlinear weights [Henrick A.K., Aslam T.D., Powers J.M.: J. Comp. Phys. 207 (2005) 542–567], which we extend up to WENO17 (r = 9). We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent CFL limitation (CFL ∈ ...

In this paper we construct high-order weighted essentially nonoscillatory (WENO) schemes for solving the nonlinear Hamilton–Jacobi equations on two-dimensional unstructured meshes. The main ideas are nodal based approximations, the usage of monotone Hamiltonians as building blocks on unstructured meshes, nonlinear weights using smooth indicators of second and higher derivatives, and a strategy ...

Abstract. We develop a locally conservative Eulerian-Lagrangian finite volume scheme with the weighted essentially non-oscillatory property (EL-WENO) in one-space dimension. This method has the advantages of both WENO and Eulerian-Lagrangian schemes. It is formally high-order accurate in space (we present the fifth order version) and essentially non-oscillatory. Moreover, it is free of a CFL ti...

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...

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization...