Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in distribution networks (WDN). Chlorine-based WQ regulation control aims to maintain pathogen-free water. residual evolution within WDN commonly modeled using the typical single-species decay reaction dynamics that account network-wide, spatiotemporal chlorine concentrations only. Prior studies have proposed mor...

The finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, the artificial compression method of Harten, and Glimm’s method, a random choice method, are discussed. The methods are used to integrate the one-dimensional Eulerian form of the equations of gas d...

this paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. the method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions.the construction of the nonstandard method is based on the special treatment of the interface using suitable jump condition...

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax–Friedrichs discretization on a uniform grid, and a key point is that the numerical sm...

In this paper, we present an intensive investigation of the finite volume method (FVM) compared to difference methods (FDMs). order show main in way approaching solution, take Burgers equation and Buckley–Leverett as examples simulate previously mentioned methods. On one hand, results using schemes Lax–Friedrichs Lax–Wendroff. other apply Godunov’s scheme method. Moreover, how starting with a v...

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the “direction of the wind.” Instead, we propose to use as a building block the mor...

In this paper, high order central finite difference schemes in a finite interval are analyzed for the diffusion equation. Boundary conditions of the initial-boundary value problem (IBVP) are treated by the simplified inverse Lax-Wendroff (SILW) procedure. For the fully discrete case, a third order explicit Runge-Kutta method is used as an example for the analysis. Stability is analyzed by both ...

One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax–Wendroff followed by one step of a diffusive scheme such as Lax–Friedrichs. We apply this idea to gas dynamics in Lagrangian coordinates. We show numerical results in two dimensions for Noh’s infinite strength shock problem and the Sedov blast wave problem, and for several one...

We investigate oneand multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave Ū(x1), x1 > 0, obtaining necessary conditions of (i) weak stability of the limiting shock, (ii) weak stability of the constant layer u ≡ U− := limz→−∞ Ū(z), and (iii) nonnegativity of a modified Lopatinski determinant similar to that of the inviscid shock ...

Abstract We discuss a high order accurate numerical boundary condition for solving hyperbolic conservation laws on fixed Cartesian grids, while the physical domain can be arbitrarily shaped and moving. Compared with body-fitted meshes, the biggest advantage of Cartesian grids is that the grid generation is trivial. The challenge is however that the physical boundary does not usually coincide wi...