Description: This proposal presents a stand-alone implicit high order temporal differencing solver concept that will interface with research and commercial numerical analysis codes to provide unlimited temporal accuracy. While the computational fluid dynamics (CFD) market has mature products that solve a large portion of problems faced by practicing engineers, these tools are often inadequate for fast transient, multi-scale numerical problems such as highly resolved turbulence, vortex shedding and combustion instability where rapid, small scale local phenomena can be overwhelmed by numerical dissipation. Many research and commercial solvers perform sufficient spatial resolution, but use insufficient explicit or low order implicit temporal resolution. Higher order explicit temporal schemes are not always feasible when modeling turbulence, can be severely limited by the time step size, and are less efficient than even low-order implicit methods. In the proposed Phase I effort, a previously developed high order implicit time integration formulation, tested up to 11th order accuracy, will be extracted from an existing solver and interfaced with an independent finite-volume solver to prove the feasibility of providing decoupled time integration for existing numerical codes. In Phase II, the time integration formulation will be implemented in a software framework and tested with readily available, popular numerical codes

Benefits: Scientists and engineers in a wide range of physical disciplines, such as mechanics, medicine, physical cosmology, nano-technology, etc., employ transient computational analysis to solve governing equations that are too difficult to solve analytically. Many of these computational disciplines require accurate transient analyses. The temporal differencing solver developed in this project will serve as an important aid for these researchers to obtain high temporal accuracy with a reasonable amount of computational effort.

Many NASA scientists and engineers are involved in the development and use of advanced numerical analysis codes for applications in physics, engineering, biotechnology, etc. This project will develop and deliver a tool for incorporating implicit higher order differencing into these computational codes, allowing high order temporal solutions without developing a new solver. Potential CFD applications include acoustics, combustion (including combustion instability), and turbulence.