Implicit Higher Order Temporal Differencing for Aeroacoustic and CFD Applications

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