Today there are a number of problems in engineering and science, which share a single common computational challenge: the ability to solve and/or model accurately and efficiently a wide range of spatial and temporal scales. Numerical simulation of such problems requires either the use of highly adaptive physics based numerical algorithms, the use of reduced models that capture “important” physics of the problem at a lower cost, or the combination of both approaches. In addition, with the rapidly increasing ability to model large problems and the constant demand to extract and visualize the information relatively quickly or even interactively, the scientific visualization of very large data sets has become a challenge in itself.

Currently we are working on development of multi-scale modeling and simulation environment capable of performing different fidelity simulations for single/multi-phase, inert/reactive, compressible/incompressible, transitional and turbulent flows in complex geometries. At the core of the problem solving environment is an integrated adaptive multi-scale/multi-form modeling and simulation framework that on-the-fly identifies regions of the flow with a suitable model-form, differentiates the most dominant (energetic) structures that control the overall dynamics of the flow; and resolves and “tracks” on a space-time adaptive mesh these dynamically-dominant flow structures, while modeling the effect of the unresolved motions using the compatible multi-level model form. The unique feature of the problem-solving environment is a unified, dynamically adaptive, wavelet multi-resolution (multi-scale), and multi-form approach to numerical algorithms and solvers, modeling and visualization.

Computational Grid (colored by processor number)

1) Schneider, K. and Vasilyev, O.V., Wavelet Methods in Computational Fluid Dynamics. Ann. Rev. Fluid

Mech., 42, pp. 473-503, 2010.

2) Nejadmalayeri, A., Vezolainen, A., Brown-Dymkoski, E., and Vasilyev, O.V., Parallel Adaptive Wavelet Collocation Method for PDEs, Journal of Computational Physics, 298, pp. 237-253, 2015.