The aim of this paper is to develop a new two dimensional time accurate Euler solver for shock tube applications. The solver was developed to study the performance of a newly built short-duration hypersonic test facility at Universiti Tenaga Nasional “UNITEN” in Malaysia. The facility has been designed, built, and commissioned for different values of diaphragm pressure ratios in order to get wi...

In problems where shock waves move slowly relative to the grid, numerical errors in density and momentum may occur at the shock and propagate downstream, thereby contaminating the solution. These errors are analyzed in the present work and a fix is proposed. The errors are divided into two classes: start-up errors and post-shock oscillations. It is shown that a traveling wave analysis of the is...

The main objective of the present study is to utilize a novel linearization strategy to linearize the convection terms of the quasi-one-dimensional Euler governing equations on collocated grids and to examine its shock-capturing capabilities. To avoid a pressure checkerboard problem on the collocated grids, it is necessary to utilize two velocity definitions at each cell face. Similarly, we def...

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwin...

The inhomogeneous Poisson (Laplace) equation with internal Dirichlet boundary conditions has recently appeared in several applications ranging from image segmentation [1–3] to image colorization [4], digital photo matting [5, 6] and image filtering [7, 8]. In addition, the problem we address may also be considered as the generalized eigenvector problem associated with Normalized Cuts [9], the l...

This paper gives a detailed analysis of the physics of simple pendulum and the equations governing the motion and velocity. The pendulum works in three modes: simple, damped and driving and driving only. The signatures are evaluated and simulated by the means of four different approaches: Euler method, Euler-Cromer method, 2 nd order Runge-kutta method and built-in ODE-23 matlab solver. The sim...

The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We report a derivation of the Parareal method that uses a convergence acceleration technique to improve the accuracy of the solution. Our approach uses firstly...