scholarly journals Hierarchical Adaptive Eddy-Capturing Approach for Modeling and Simulation of Turbulent Flows

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 83
Author(s):  
Giuliano De Stefano ◽  
Oleg V. Vasilyev
Keyword(s):  
Modeling And Simulation ◽  
Collocation Method ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Adaptive Methods ◽  
Short Review ◽  
Wavelet Thresholding ◽  
Modeling Framework ◽  
Adaptive Wavelet ◽  
Wavelet Collocation Method

A short review of wavelet-based adaptive methods for modeling and simulation of incompressible turbulent flows is presented. Wavelet-based computational modeling approaches of different fidelities are recast into an integrated hierarchical adaptive eddy-capturing turbulence modeling framework. The wavelet threshold filtering procedure and the associated wavelet-filtered Navier–Stokes equations are briefly discussed, along with the adaptive wavelet collocation method that is used for numerical computations. Depending on the level of wavelet thresholding, the simulation is possibly supplemented with a localized closure model. The latest advancements in spatiotemporally varying wavelet thresholding procedures along with the adaptive-anisotropic wavelet-collocation method make the development of a fully adaptive approach feasible with potential applications for complex turbulent flows.

scholarly journals Computational Fluid Dynamics Using the Adaptive Wavelet-Collocation Method

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 377
Author(s):  
Yash Mehta ◽  
Ari Nejadmalayeri ◽  
Jonathan David Regele
Keyword(s):  
Boundary Conditions ◽  
Collocation Method ◽  
High Efficiency ◽  
Adaptive Methods ◽  
Immersed Boundary ◽  
Adaptive Wavelet ◽  
Wavelet Collocation Method ◽  
External Flows ◽  
Active Research ◽  
Dynamic Adaptability

Advancements to the adaptive wavelet-collocation method over the last decade have opened up a number of new possible areas for active research. Volume penalization techniques allow complex immersed boundary conditions to be used with high efficiency for both internal and external flows. Anisotropic methods make it possible to use body-fitted meshes while still taking advantage of the dynamic adaptability properties wavelet-based methods provide. The parallelization of the approach has made it possible to perform large high-resolution simulations of detonation initiation and fluid instabilities to uncover new physical insights that would otherwise be difficult to discover. Other developments include space-time adaptive methods and nonreflecting boundary conditions. This article summarizes the work performed using the adaptive wavelet-collocation method developed by Vasilyev and coworkers over the past decade.

An Adaptive Wavelet Collocation Method for Solution of the Convection-Dominated Problem on a Sphere

2018 ◽  
Vol 15 (08) ◽  
pp. 1850080
Author(s):  
Ratikanta Behera ◽  
Mani Mehra
Keyword(s):  
Numerical Simulation ◽  
Collocation Method ◽  
Second Generation ◽  
Efficient Computation ◽  
Adaptive Wavelet ◽  
Spherical Wavelets ◽  
Collocation Points ◽  
Wavelet Collocation Method ◽  
Uniform Grids ◽  
Convection Dominated

In this paper, we present a numerical simulation of a convection-dominated problem using adaptive wavelet collocation method. This is based on second-generation spherical wavelets on a recursively refined spherical geodesic grid. The power lies in the fact that they only require small number of coefficients to represent this problem more accurately, which allows compression and efficient computation. In contrast with other approximate schemes, this approach reduced the number of collocation points used by factors of many orders of magnitude when compared to uniform grids of equivalent resolution. Numerical results demonstrate the efficiency of our approach.

An Adaptive Wavelet Method for the Incompressible Navier-Stokes Equations in Complex Domains

2004 ◽  
Author(s):  
Damrongsak Wirasaet ◽  
Samuel Paolucci
Keyword(s):  
Stokes Equations ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Adaptive Wavelet ◽  
Brinkman Equations ◽  
Wavelet Collocation Method ◽  
Alternative Means ◽  
Interpolating Wavelets ◽  
Solid Obstacles

An adaptive wavelet-based method provides an alternative means to refine grids according to local demands of the physical solution. One of the prominent challenges of such a method is the application to problems defined on complex domains. In the case of incompressible flow, the application to problems with complicated domains is made possible by the use of the Navier-Stokes/Brinkman equations. These equations take into account solid obstacles by adding a penalized velocity term in the momentum equation. In this study, an adaptive wavelet collocation method, based on interpolating wavelets, is first applied to a benchmark problem defined on a simple domain to demonstrate the accuracy and efficiency of the method. Then the penalty technique is used to simulate flows over obstacles. The numerical results are compared with those obtained by other computational approaches as well as with experiments.

scholarly journals Adaptive wavelet collocation method on the shallow water model

2014 ◽  
Vol 271 ◽  
pp. 342-359 ◽  
Author(s):  
Shanon M. Reckinger ◽  
Oleg V. Vasilyev ◽  
Baylor Fox-Kemper
Keyword(s):  
Shallow Water ◽  
Collocation Method ◽  
Water Model ◽  
Shallow Water Model ◽  
Adaptive Wavelet ◽  
Wavelet Collocation Method
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