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Current Research Topics
Adaptive Wavelet Environment for in Silico Universal Multiscale Modeling (AWESUMM)
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.
Hierarchical Eddy-Resolving Approach for Turbulent Flow Simulations
Since the inception of Computational Fluid Dynamics, turbulence modeling and numerical methods evolved as two separate fields of research with the perception that once a turbulence model is developed, any suitable computational approach can be used for its implementation. The current research represents a cardinally different philosophy in its belief that in order to significantly increase the computational efficiency of turbulent flow simulations and improve the accuracy of predictions of flow characteristics, all the numerics, mesh generation and physics-based modeling need to be tightly integrated to ensure better capturing of the flow physics on a near optimal adaptive anisotropic computational grid, ultimately leading to substantial reduction in the computational cost, while resolving dynamically dominant flow structures. Latest advancements in wavelet-based adaptive multi-resolution methodologies for the solution of partial differential equations, combined with the unique properties of wavelet analysis to unambiguously identify and isolate localized dynamically dominant flow structures, make it feasible to develop a new framework for hierarchical modeling and simulation of turbulent flows that fully utilizes spatial/temporal turbulent flow intermittency and tightly integrates numerics and physics-based modeling.
The overall goal of the project is to develop an innovative, robust and computationally efficient predictive computational approach, capable of performing numerical simulation of transitional and turbulent compressible flows for different flow conditions, including turbulent flow separation, turbulent boundary layers, shear layers, and jets. The computational technology currently being developed has a potential to revolutionize the field of computational modeling in industrial applications involving complex turbulent flows with ultimate objective to develop a reliable and affordable predictive simulation-based tools that can be used in the design of fluids engineering systems and/or their components.
Parallel Adaptive-Anisotropic Wavelet Collocation Method
(A-AWCM) for Solution of Multi-Scale Problems
Four approaches for solving nonlinear partial differential equations adaptively have been developed. Each method uses the adaptive wavelet collocation method (AWCM) based on bi-orthogonal lifted interpolating wavelets to construct a computational grid adapted to the solution. The wavelet decomposition naturally provides a set of nested multi-scale grids adapted to the solution, and we take advantage of this property in developing our methods. In the first two methods we implement a traditional time marching scheme for parabolic and hyperbolic partial differential equations, but use AWCM to adapt the computational grid to the solution at each time step. When hyperbolic equations are solved an additional wavelet-based procedure for shock capturing is used. With this procedure the mesh is refined in the vicinity of the shock up to a-priori specified resolution and the shock is smoothed out using localized numerical viscosity. The third method simply uses the multi-scale wavelet decomposition as the basis for an adaptive multilevel method for nonlinear elliptic equations. Finally, we have begun to investigate a combination of the first three approaches to produce an adaptive simultaneous space time method. In this case, both the space-time grid adapts locally to the solution, and the final solution is obtained simultaneously in the entire space-time domain of interest. Our current efforts are focused on development of computational capabiliites for adaptive anisotropic complex geometry mesh generation within the framework of the Adaptive-Anisotropic Wavelet Collocation Method (A-AWCM) and improving the parallel efficiency of the solver.
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