We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea presented method is to exploit and approximate mixed spatial-temporal derivative that occurs naturally when deriving some second order accurate schemes in time. Such an approach introduced context Lax-Wendroff (or Cauchy-Kowalevski) procedure time not completely replaced by space der...

Goal of this thesis is to study four problems. In chapters 3-5, we consider scalar conservation law in one space dimension with strictly convex flux. First problem is to know the profile of the entropy solution. In spite of the fact that, this was studied extensively in last several decades, the complete profile of the entropy solution is not well understood. Second problem is the exact control...

This paper introduces the use of moving least-squares (MLS) approximations for the development of high-order finite volume discretizations on unstructured grids. The field variables and their successive derivatives can be accurately reconstructed using this mesh-free technique in a general nodal arrangement. The methodology proposed is used in the construction of two numerical schemes for the s...

In this paper, the Lax-Wendroff difference scheme has been presented for solving one-dimensional wave equation with integral boundary conditions. First, given solution domain is discretized and derivative involving spatial variable replaced by central finite approximation of functional values at each grid point using Taylor series expansion. Then, resulting second-order linear ordinary differen...

The problem of traffic congestion is becoming endemic due to increased levels of populations owning automobiles. In an effort to minimize congestion, an accurate method for modeling the flow of traffic is imperative. While randomized microscopic models can be very accurate, they are computationally much slower than macroscopic models. Furthermore, macroscopic models can be very accurate in mode...

In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by Watari and Tsutahara [Phys Rev E 67,036306(2003)], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosi...

An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier–Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum....

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 ...

This paper presents a chemical species transport model to account for variable composition and gas properties along the flow path in internal combustion engines. It is described the numerical solution to adapt the gas dynamic model to chemical species transport in boundary conditions by means of the Method of Characteristics and in volumes by means of a filling and emptying model. The performan...