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Dr. Yury Gryazih

Institution: Idaho State University

Department: Mathematics & Statistics

Proposed research ideas:

Recent results on the numerical simulation of classical turbulent flow over a heated plane suggest that the implicit dissipation of the numerical schemes can lead to artificial convective structures similar to naturally realized Rayleigh-Bernard cells in the simulated flows. These structures are artificial for the specified range of parameters. These results demonstrate the importance of the use of high-resolution non-oscillatory schemes in the numerical simulation of the atmospheric boundary layer turbulent flows. In this project we will consider the application of WENO(weighted essentially non-oscillatory) – type schemes in the implicit large-eddy-simulation of the cumulus convection. The project will focus on the three major part of the problem: 1) Development of a high-resolution non-oscillatory conservative scheme for incompressible turbulent flows. Practically, every scheme of this class is based on switching the underlying stencils according to the gradient of the simulated flows. Usually such schemes introduce additional numerical dissipation to preserve monotonicity of the numerical solution of the numerical solution of hyperbolic conservation laws, i.e. in the simulation of the inviscid flows. The direct application of these schemes to turbulent flow simulation may introduce excessive numerical dissipation and as a result cause a poor performance of the turbulent model. The development of the adjustment strategy for the WENO-type high-resolution schemes will be the first major part of the project. 2) The second part of the proposed research is the efficient numerical implementation of implicit finite-volume schemes based on the scalable Parallel Krylov subspaces type method with FFT(Fast Fourier Transform) preconditioner. This approach exhibits excellent convergence properties in the case of the numerical solution of the Helmholtz equation. This provides hope that such an approach will be a good choice for a solver in the case of implicit schemes for simulations of incompressible turbulent flows. 3) The focus of the third part of the project will be on the comparison of the simulation results of the dynamics of the cumulus-topped boundary layer with existing simulated and observed results. The successful application of the developed numerical approach to the simulation of the small-scale turbulent atmospheric flows associated with clouds and thermals is the ultimate goal of the proposed research.


It will provide an opportunity to work with the world leading computational group in the research area.