Engineering topics

Woodward, C. S.

Publications and source records attributed to Woodward, C. S..

3 records

DOE OSTI2019

Multirate Time Integration for ODEs and DAEs (Final Report)

This project investigated multirate time integration methods. These methods evolve a differential equation system in time by advancing parts of the problem with fast time scales at small time steps and parts of the problem with slow time scales with larger time steps. The project developed new methods and theory as well as a set of prototype software implementations. Multirate methods were tested on combustion and climate applications. A series of five presentations were given on project results and two papers are planned.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Progress in fast, accurate multi-scale climate simulations

We present a survey of physical and computational techniques that have the potential to contribute to the next generation of high-fidelity, multi-scale climate simulations. Examples of the climate science problems that can be investigated with more depth with these computational improvements include the capture of remote forcings of localized hydrological extreme events, an accurate representation of cloud features over a range of spatial and temporal scales, and parallel, large ensembles of simulations to more effectively explore model sensitivities and uncertainties. Numerical techniques, such as adaptive mesh refinement, implicit time integration, and separate treatment of fast physical time scales are enabling improved accuracy and fidelity in simulation of dynamics and allowing more complete representations of climate features at the global scale. At the same time, partnerships with computer science teams have focused on taking advantage of evolving computer architectures such as many-core processors and GPUs. As a result, approaches which were previously considered prohibitively costly have become both more efficient and scalable. In combination, progress in these three critical areas is poised to transform climate modeling in the coming decades.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

Implicit integration methods for dislocation dynamics

In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a way of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.

36 MATERIALS SCIENCE↗