A methodology of multi-dimensional physics simulations is investigated based on a data-driven learning algorithm derived from proper orthogonal decomposition (POD). The approach utilizes numerical simulation tools to collect solution data for the problems of interest subjected to parametric variations that may include interior excitations and/or boundary conditions influenced by exterior environments. The POD is applied to process the data and to generate a finite set of basis functions. The problem is then projected from the physical domain onto a mathematical space constituted by its basis functions. The effectiveness of the POD methodology thus depends on the data quality, which relies on the numerical settings implemented in the data collection (or the training). The simulation methodology is developed and demonstrated in a dynamic heat transfer problem for an entire CPU and in a quantum eigenvalue problem for a quantum-dot structure. Encouraging findings are observed for the POD simulation methodology in this investigation, including its extreme efficiency, high accuracy and great adaptability. The models constructed by the POD basis functions are even capable of predicting the solution of the problem beyond the conditions implemented in the training with a good accuracy.
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Thermal Simulation of a CPU Based on Model Order Reduction
A previously developed thermal simulation technique based on model order reduction is applied to the simulation of a CPU. The approach is derived from proper orthogonal decomposition (POD) that projects the physical domain onto the POD space. It has been demonstrated that the developed approach offers an accurate thermal simulation of the CPU with a reduction in numerical degrees of freedom by several orders of magnitude compared to the direct numerical simulation (DNS). In addition, the technique has the capability of providing spatial resolution as fine as the direct numerical simulation for the CPU.
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- Award ID(s):
- 1852102
- NSF-PAR ID:
- 10200426
- Date Published:
- Journal Name:
- IEEE MIT Undergraduate Research Technology Conference 2020
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM). This is a regularized ROM (Reg‐ROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convection‐dominated flows. We also consider the Leray ROM (L‐ROM). These two Reg‐ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four Reg‐ROM/filter combinations are tested in the numerical simulation of the three‐dimensional flow past a circular cylinder at a Reynolds number
R e =1000. Overall, the most accurate Reg‐ROM/filter combination is EF‐ROM‐DF. Furthermore, the spatial filter has a higher impact on the Reg‐ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF‐ROM and L‐ROM. Finally, the CPU times of the four Reg‐ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd. -
We introduce Aquila-LCS, GPU and CPU optimized object-oriented, in-house codes for volumetric particle advection and 3D Finite-Time Lyapunov Exponent (FTLE) and Finite-Size Lyapunov Exponent (FSLE) computations. The purpose is to analyze 3D Lagrangian Coherent Structures (LCS) in large Direct Numerical Simulation (DNS) data. Our technique uses advanced search strategies for quick cell identification and efficient storage techniques. This solver scales effectively on both GPUs (up to 62 Nvidia V100 GPUs) and multi-core CPUs (up to 32,768 CPU cores), tracking up to 8-billion particles. We apply our approach to four turbulent boundary layers at different flow regimes and Reynolds numbers.more » « less
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Abstract Uvula‐induced snoring and associated obstructive sleep apnea is a complex phenomenon characterized by vibrating structures and highly transient vortex dynamics. This study aimed to extract signature features of uvula wake flows of different pathological origins and develop a linear reduced‐order surrogate model for flow control. Six airway models were developed with two uvula kinematics and three pharynx constriction levels. A direct numerical simulation (DNS) flow solver based on the immersed boundary method was utilized to resolve the wake flows induced by the flapping uvula. Key spatial and temporal responses of the flow to uvula kinematics and pharynx constriction were investigated using continuous wavelet transform (CWT), proper orthogonal decomposition (POD), and dynamic mode decomposition (DMD). Results showed highly complex patterns in flow topologies. CWT analysis revealed multiscale correlations in both time and space between the flapping uvular and wake flows. POD analysis successfully separated the flows among the six models by projecting the datasets in the vector space spanned by the first three eigenmodes. Perceivable differences were also captured in the time evolution of the DMD modes among the six models. A linear reduced‐order surrogate model was constructed from the predominant eigenmodes obtained from the DMD analysis and predicted vortex patterns from this surrogate model agreed well with the corresponding DNS simulations. The computational and analytical platform presented in this study could bring a variety of applications in breathing‐related disorders and beyond. The computational efficiency of surrogate modeling makes it well suited for flow control, forecasting, and uncertainty analyses.
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Purpose The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry). Design/methodology/approach This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is the same for homogeneous and heterogeneous materials (the difference in the values of the stencil coefficients). The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of OLTEM at a given stencil width. The numerical results with irregular interfaces show that at the same number of degrees of freedom, OLTEM with the 9-points stencils is even more accurate than the 4-th order finite elements; OLTEM with the 25-points stencils is much more accurate than the 7-th order finite elements with much wider stencils and conformed meshes. Findings The significant increase in accuracy for OLTEM by one order for 'linear' elements and by 8 orders for 'quadratic' elements compared to that for known techniques. This will lead to a huge reduction in the computation time for the problems with complex irregular interfaces. The use of trivial unfitted Cartesian meshes significantly simplifies the solution and reduces the time for the data preparation (no need in complicated mesh generators for complex geometry). Originality/value It has been never seen in the literature such a huge increase in accuracy for the proposed technique compared to existing methods. Due to a high accuracy, the proposed technique will allow the direct solution of multiscale problems without the scale separation.more » « less
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