Application of integration algorithms in a parallel processing environment for the simulation of jet engines

The application of Predictor corrector integration algorithms developed for the digital parallel processing environment are investigated. The algorithms are implemented and evaluated through the use of a software simulator which provides an approximate representation of the parallel processing hardware. Test cases which focus on the use of the algorithms are presented and a specific application using a linear model of a turbofan engine is considered. Results are presented showing the effects of integration step size and the number of processors on simulation accuracy. Real time performance, interprocessor communication, and algorithm startup are also discussed

One step multiderivative methods for first order ordinary differential equations

A family of one-step multiderivative methods based on Padé approximants to the exponential function is developed. The methods are extrapolated and analysed for use in PECE mode. Error constants and stability intervals are calculated and the combinations compared with well known linear multi-step combinations and combinations using high accuracy Newton-Cotes quadrature formulas as correctors. w926020

An intelligent processing environment for real-time simulation

The development of a highly efficient and thus truly intelligent processing environment for real-time general purpose simulation of continuous systems is described. Such an environment can be created by mapping the simulation process directly onto the University of Alamba's OPERA architecture. To facilitate this effort, the field of continuous simulation is explored, highlighting areas in which efficiency can be improved. Areas in which parallel processing can be applied are also identified, and several general OPERA type hardware configurations that support improved simulation are investigated. Three direct execution parallel processing environments are introduced, each of which greatly improves efficiency by exploiting distinct areas of the simulation process. These suggested environments are candidate architectures around which a highly intelligent real-time simulation configuration can be developed

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency

On the Numerical Stability of Simulation Methods for SDES

When simulating discrete time approximations of solutions of stochastic differential equations (SDEs), numerical stability is clearly more important than numerical efficiency or some higher order of convergence. Discrete time approximations of solutions of SDEs are widely used in simulations in finance and other areas of application. The stability criterion presented is designed to handle both scenario simulation and Monte Carlo simulation, that is, strong and weak simulation methods. The symmetric predictor-corrector Euler method is shown to have the potential to overcome some of the numerical instabilities that may be experienced when using the explicit Euler method. This is of particular importance in finance, where martingale dynamics arise for solutions of SDEs and diffusion coefficients are often of multiplicative type. Stability regions for a range of schemes are visualized and discussed. For Monte Carlo simulation it turns out that schemes, which have implicitness in both the drift and the diffusion terms, exhibit the largest stability regions. It will be shown that refining the time step size in a Monte Carlo simulation can lead to numerical instabilities.stochastic differential equations; scenario simulation; Monte Carlo simulation; numerical stability; predictor-corrector methods; implicit methods

Finite-difference methods for simulation models incorporating non-conservative forces

We discuss algorithms applicable to the numerical solution of second-order ordinary differential equations by finite-differences. We make particular reference to the solution of the dissipative particle dynamics fluid model, and present extensive results comparing one of the algorithms discussed with the standard method of solution. These results show the successful modeling of phase separation and surface tension in a binary immiscible fluid mixture.Comment: 27 pages RevTeX, 9 figures, J. Chem. Phys. (in press

The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories

An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered