The fully Lagrangian approach to the analysis of particle/droplet dynamics: Implementation into ansys fluent and application to gasoline sprays

The fully Lagrangian approach (FLA) to the calculation of teh number density of inertial partucles in dilute gas-particles flows was incorporated into teh CFD code ANSYS Flunet. The new verion of ANSYS Fluent was applied to moedling dilute gas-particle flow around a cylinder and liquid droplets in a gasoline fuel spray. In a steady-state case, thre predictions of the FLA for the flow around a cylinder and those based on teh equilibrium Eulerian method (EE) are almost the same for small Stokes number (Stk) and small Reynolds number (Re). FLA predicts higher values of the gradients of particle number densities in front of the cylinder compared with the ones predicted by the EE for larger values of Stk and Re. Application of FLA to a direct injection gasoline fuel spray has concentrated on the computation of the number densities of droplets. Results revelaed good agreement between the numerical simulation and exeperimental data

The effect of FPU architecture on a dynamic precision algorithm for the solution of differential equations

Solution of lnitial Value Problems (IVPs) is an important application in scientific computing. Methods for solving these problems use techniques for reducing the error and increasing the speed of the computation. This paper introduces a class of algorithms which dynamically reconfigure their operating parameters to reduce the computation time. By dynamically varying the precision of the arithmetic being performed, it is possible to obtain dramatic speedups on certain architectures when solving IVPs. This paper illustrates how various architectures impact on a dynamic precision version of the Runge-Kutta-Fehlberg algorithm. It is shown that a speedup of over 30 percent is possible for both massively parallel processors and vector supercomputers

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code.Comment: 9 pages, 5 figure

Numerical Solutions of Nonlinear Ordinary Differential Equations by Using Adaptive Runge-Kutta Method

We present a study on numerical solutions of nonlinear ordinary differential equations by applying Runge-Kutta-Fehlberg (RKF) method, a well-known adaptive Runge-kutta method. The adaptive Runge-kutta methods use embedded integration formulas which appear in pairs. Typically adaptive methods monitor the truncation error at each integration step and automatically adjust the step size to keep the error within prescribed limit. Numerical solutions to different nonlinear initial value problems (IVPs) attained by RKF method are compared with corresponding classical Runge-Kutta (RK4) approximations in order to investigate the computational superiority of the former. The resulting gain in efficiency is compatible with the theoretical prediction. Moreover, with the aid of a suitable time-stepping scheme, we show that the RKF method invariably requires less number of steps to arrive at the right endpoint of the finite interval where the IVP is being considered