A second order front tracking method is developed for solving the Euler equations of in-viscid fluid dynamics numerically. Front tracking methods are usually limited to first order accuracy, since they are based on a piecewise constant approximation of the solution. Here the second order

Summary. Front tracking methods can be used to accurately resolve discontinu-ities in numerical simulations of Euler flows. They usually result in first-order error convergence due to their piecewise constant approximation of the flow conditions. In this chapter, a piecewise linear reconstruction

not distinguish between moving shadows and moving objects. This paper presents a method which improves this adaptive background mixture model. By reinvestigating the update equations, we utilise different equations at different phases. This allows our system learn faster and more accurately as well as adapt

A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general non-linear measurement equation in position. A general algorithm is presented, which is parsimonious

We discuss how to combine a front tracking method with dimensional splitting to solve numerically systems of conservation laws in two space dimensions. In addition we present an adaptive grid refinement strategy. The method is unconditionally stable and allows for moderately high cfl numbers

to this higher dimensional level set function. This paper applies Sethian's Fast Marching Method, which is a very fast technique for solving the Eikonal and related equations, to the problem of building fast and appropriate extension velocities for the neighboring level sets. Our choice and construction

. We describe a three dimensional front tracking algorithm, discuss its numerical implementation, and present studies to validate the correctness of this approach. Based on the results of the two dimensional computations, we expect three dimensional front tracking to improve significantly

We present a new method for stability and modal analysis of shear flows and their acous-tic radiation. The Euler equations are modified and solved as a spatial initial value problem in which initial perturbations are specified at the flow inlet and propagated downstream by integration

A level set formulation is derived for incompressible, immiscible smooths out the front. In the case of irrotational flow, one Navier–Stokes equations separated by a free surface. The interface can reformulate the problem in the boundary integral form is identified as the zero level set of a

of stiffness of common problems in combustion processes. Numerical results for Majda’s model and reactive Euler equations in one and two dimensions show substantially improved efficiency over traditional methods.