The purpose of this paper is twofold. Firstly we carry out an extension of the fully discrete third order TVD scheme, for linear case, presented in [8] to nonlinear scalar hyperbolic conservation laws for one and two dimensions. Secondly, we propose a semi-discrete version of the scheme. Time evolution is carried out by the third order TVD RungeKutta method. The advantages of the scheme are its...

Nessyahu and Tadmor s central scheme [J. Comput. Phys. 87 (1990)] has the benefit of not using Riemann solvers for solving hyperbolic conservation laws. But the staggered averaging causes large dissipation when the time step size is small compared to the mesh size. The recent work of Kurganov and Tadmor [J. Comput. Phys. 160 (2000)] overcomes this problem by using a variable control volume and ...

This paper formulates and analyzes fully discrete schemes for the two-dimensional Keller-Segel chemotaxis model. The spatial discretization of the model is based on the discontinuous Galerkin methods and the temporal discretization is based either on Forward Euler or the second order explicit total variation diminishing (TVD) Runge-Kutta methods. We consider Cartesian grids and prove optimal fu...

The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known TVD and NVD families of diierencing schemes. All of those use some sort of an \unboundedness indicator" in order to determine the parts of the domain where intervention in the discretisati...

In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally 1 contracting and TVD. However, the Caputo derivative leads to the modified CFL-type stability condition, ( t) = O( x...

In the literature, much attention has been paid to Runge-Kutta methods (RKMs) satisfying special nonlinear stability requirements indicated by the terms total-variation-diminishing (TVD), strong stability preserving (SSP) and monotonicity. Stepsize conditions, guaranteeing these properties, were derived by Shu and Osher [J. Comput. Phys., 77 (1988) pp. 439-471] and in numerous subsequent papers...

This paper describes the development of the stream-tube based dispersion model for modeling contaminant transport in open channels. The operator-splitting technique is employed to separate the 2D contaminant transport equation into the pure advection and pure dispersion equations. Then the total variation diminishing (TVD) schemes are combined with the second-order Lax-Wendroff and third–order ...

The purpose of this research is to develop a new torque vectoring differential (TVD) for vehicle applications and investigate its effect on vehicle dynamic control. TVD is a technology that is able to distribute the engine torque to the left and right driving wheels at different ratios so that the yaw motion control can be realized. Attention has been paid to this technology in recent years bec...

A conservative modification to the ghost fluid method (GFM) is developed for compressible multiphase flows. The motivation is to eliminate or reduce the conservation error of the GFM without affecting its performance. We track the conservative variables near the interface and use this information to modify the numerical solution when the interface has passed the cell. The modification procedure...