A Boundary Element Method for Three-Dimensional Steady Convective Heat Diffusion

2004 ◽  
Author(s):  
M. M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Convective Heat ◽  
Sparse Matrices ◽  
Three Dimensional ◽  
Higher Order ◽  
Iterative Solvers ◽  
Boundary Element Methods ◽  
Heat Diffusion ◽  
Element Formulation ◽  
Definition Of

Higher-order boundary element methods (BEM) are presented for three-dimensional steady convective heat diffusion at high Peclet numbers. An accurate and efficient boundary element formulation is facilitated by the definition of an influence domain due to convective kernels. This approach essentially localizes the surface integrations only within the domain of influence which becomes more narrowly focused as the Peclet number increases. The outcome of this phenomenon is an increased sparsity and improved conditioning of the global matrix. Therefore, iterative solvers for sparse matrices become a very efficient and robust tool for the corresponding boundary element matrices. In this paper, we consider an example problem with an exact solution and investigate the accuracy and efficiency of the higher-order BEM formulations for high Peclet numbers in the range from 1,000 to 100,000. The bi-quartic boundary elements included in this study are shown to provide very efficient and extremely accurate solutions, even on a single engineering workstation.

A Higher-Order Poly-Region Boundary Element Method for Steady Thermoviscous Fluid Flows

2004 ◽  
Author(s):  
M. . M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Boundary Integral Equations ◽  
Fluid Flows ◽  
Boundary Elements ◽  
Higher Order ◽  
Boundary Integral ◽  
Iterative Solvers ◽  
Boundary Element Methods ◽  
Element Formulation ◽  
Thermoviscous Fluid

In this presentation, we re-visit the poly-region boundary element methods (BEM) proposed earlier for the steady Navier-Stokes [1] and Boussinesq [2] flows, and develop a novel higher-order BEM formulation for the thermoviscous fluid flows that involves the definition of the domains of kernel influences due to steady Oseenlets. We introduce region-by-region implementation of the steady-state Oseenlets within the poly-region boundary element fequatramework, and perform integration only over the (parts of) higher-order boundary elements and volume cells that are influenced by the kernels. No integration outside the domains of the kernel influences are needed. Owing to the properties of the convective Oseenlets, the kernel influences are very local and propagate upstream. The localization becomes more prominent as the Reynolds number of the flow increases. This improves the conditioning of the global matrix, which in turn, facilitates an efficient use of the iterative solvers for the sparse matrices [3]. Here, we consider quartic boundary elements and bi-quartic volume cells to ensure a high level resolution in space. Similar to the previous developments [4–6], coefficients of the discrete boundary integral equations are evaluated with the sufficient precision using semi-analytic approach to ensure exceptional accuracy of the boundary element formulation. To demonstrate the attractiveness of the poly-region BEM formulation, we consider a numerical example of the well-known Rayleigh-Benard problem governed by the Boussinesq equations.

Multi-Level Boundary Element Methods for Steady Heat Diffusion in Three-Dimensions

2005 ◽  
Author(s):  
M. M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
Three Dimensions ◽  
Heat Diffusion ◽  
Numerical Heat Transfer ◽  
Multi Level ◽  
Solution Accuracy ◽  
Steady Heat

We have recently developed a novel multi-level boundary element method (MLBEM) for steady heat diffusion in irregular two-dimensional domains (Numerical Heat Transfer Part B: Fundamentals, 46: 329–356, 2004). This presentation extends the MLBEM methodology to three-dimensional problems. First, we outline a 3-D MLBEM formulation for steady heat diffusion and discuss the differences between multi-level algorithms for two and three dimensions. Then, we consider an example problem that involves heat conduction in a semi-infinite three-dimensional domain. We investigate the performance of the MLBEM formulation using a single-patch approach. The MLBEM algorithms are shown facilitate fast and accurate numerical solutions with no loss of the solution accuracy. More dramatic speed-ups can be achieved provided that patch-edge corrections are also evaluated using multi-level technique.

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

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