Accurate, Efficient, and Robust Adaptive Solution Methods and Models for Predicting Multi-Scale Physically-Complex Flows

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With the significant improvements in numerical methods over the last 15-20 years and correspondoing increases high-performance computing (HPC) resources, computational fluid dynamics (CFD) has become an important enabling technology in science and engineering. However, despite these advances, there remain a variety of multi-scale, physically-complex flows that are still poorly understood and have proven to be very challenging to predict by computational methods. Such flows would include but are not limited to: (i) turbulent, reactive, and multi-phase flows encountered in advanced aerospace propulsion systems; (ii) high-speed flows of gases and conducting fluids and plasmas; and (iii) micro-scale and/or rarefied non-equilibrium flows. In order to enable the more routine solution of such flows in a predictive manner, further and rather significant advances in numerical methods and CFD algorithm design are required, along with improved mathematical models for the relevant physical processes. For the latter, mathematical models that offer significant reductions in the complexity while retaining solution fidelity would be extremely desirable. The proposed research will therefore focus on the development and application of novel, accurate, efficient, and robust adaptive solution methods and models for describing multi-scale physically-complex flows using HPC architectures. Key elements of the research will include: (i) the development of output-based anisotropic adaptive mesh refinement (AMR) techniques for complex geometries and interfaces using multi-block body-fitted and hybrid grids; (ii) the enhancement of high-order finite-volume and related flux-reconstruction spatial discretization methods coupled with complementary high-order temporal discretization schemes for improved solution accuracy; (iii) the development and efficient solution of improved mathematical models based on moment closures for various transport phenomena, including non-equilibrium gaseous and plasma flows, multi-phase atomization and spray formation, the formation, oxidation, and transport of nanoscale solid soot particulates, and radiative heat transfer in participating media; and (iv) the development and exploitation of a combination of parameter estimation, data-driven, and possibly data-assimilation techniques for both assessing and improving physical models and improving simulation predictions. The potential, capabilities, and performance of the proposed computational tools for multi-scale, physically-complex problems will be assessed through application to the prediction of reactive and multi-phase flows, non-equilibrium gaseous flows, as well as high-speed space plasma flows. The latter would include the simulation of space weather phenomena. The proposed research is expected to result in a more that one order of magnitude improvement in computational efficiency compared to existing methods, thereby enabling the simulation of a far wider range of flows.