Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms. In our earlier work [31–33], we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms. In this paper, we present a different approach to the same purpose: designing high order well-balanced finite volume weight...

The typical equation for bed level change in sediment transport in river, estuary and near shore systems is based on conservation of sediment mass. It is generally a nonlinear conservation equation for bed level. The physics here are similar to shallow water wave equations and gas dynamics equation which will develop shock waves in many circumstances. Many state-of-art morphological models use ...

Two-dimensional simulations of the single-mode Richtmyer–Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005 Phys. Fluids 17 034105). The employed adaptive central-upwind sixth-order weighted essentially non-oscillatory (WENO) scheme (Hu X Y et al 2010 J. Comput. Phys. 229 8952–65) introduces only very small numerical dissipation while preser...

In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high order non oscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe s...

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on variou...

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar conservation laws with stiff source terms by extending the idea in Zhang and Shu [39]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical...

In this paper, we consider several high order schemes in one space dimension. In particular, we compare the second order relaxation (<<1) or "relaxed" (=0) schemes of Jin-Xin 4], with the second order Lax-Friedrichs scheme of Nessyahu-Tadmor 6], and with higher order ENO and WENO schemes. This comparison is rst made on Sod shock tube, and then on a very pathological example of a p-system constr...

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high accuracy at a fraction of the cost volume WENO or DG scheme comparable accuracy. This makes them quite attractive several science and engineering applications. But, to best our knowledge, such not extended non-linear hyper...

Modeling transient CO2 two-phase flow in a pipe is essential studying depressurization mechanisms resulting from liquified accidental release. Generated data such models predict the released characteristics and possible propagating fractures. Accordingly, they provide valuable input for risk prevention designing safely operating transport pipelines. simulation involves fluid-mechanical thermody...