Direct Design Solution of the Elliptic Grid Generation Equations

Ashrafizadeh, Ali; Raithby, G. D.

doi:10.1080/10407790600599009

Cited by 12 publications

(8 citation statements)

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“…The direct design approach has successfully been implemented in the context of heat conductor design, [42] various duct designs, [2] airfoil design [43] and even elliptic grid design. [44] Taiebi-Rahni et al [45] have used the direct design approach to solve internal flow shape design problems in the context of Euler equations. While most of the fully-coupled formulations in the context of direct design are well posed, there are situations that the coefficient matrix in the final discrete set might need conditioning.…”

Section: Inverse Problems In Science and Engineeringmentioning

confidence: 99%

Inverse shape design via a new physical-based iterative solution strategy

Nikfar

Ashrafizadeh

Mayeli

2014

Inverse Problems in Science and Engineering

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Inverse shape design in the context of fluid flow problems is commonly referred to the determination of the boundary shape corresponding to a given target surface pressure. Designers naturally turn to this class of problems whenever there are concerns regarding pressure-related phenomena such as cavitation, separation, shock waves, surface loading, etc. Numerical solution is often unavoidable and, therefore, three computational tools, i.e. a grid generator, a flow field solver and a shape updater, are required in an iterative solution procedure. In all existing iterative inverse design methods, the shape updater comes from separate mathematical or physical considerations that are not derived solely from the equations governing the flow field. In this paper, the currently used strategies to solve inverse shape design problems are categorized and reviewed, and then a truly physical-based iterative inverse shape design method is introduced in which the governing equations are not only used in the flow solver, but are also employed to update the shape. To explore the features of the proposed method, it is used to solve a number of shape design problems. The previously developed direct shape design method and a typical iterative solution approach are also explained and used for the solution of the same problems for the purpose of comparison. Computational results reveal that the proposed algorithm has a two to three times faster convergence rate as compared to the iterative algorithm. The convergence rate of the proposed algorithm usually stalls after three or two orders of magnitude reduction of the residual. For the test cases in this study, the direct design method is the fastest and most accurate method as compared to other algorithms. Both inhouse developed computer codes and commercial software are used as a field solver to show the general applicability of the proposed method in its current state of development.

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Section: Inverse Problems In Science and Engineeringmentioning

confidence: 99%

Inverse shape design via a new physical-based iterative solution strategy

Nikfar

Ashrafizadeh

Mayeli

2014

Inverse Problems in Science and Engineering

View full text Add to dashboard Cite

show abstract

“…   Q yy , are calculated at all nodes adjacent to the boundary using the paving layers as explained in (Ashrafizadeh & Raithby, 2006). These boundary data are then interpolated differentially as follows:…”

Section: The Dd1 Methodsmentioning

confidence: 99%

“…Equations (5) and (6) Ashrafizadeh and Raithby (Ashrafizadeh & Raithby, 2006) have shown that the TTM grid generation equations, i.e. Eqs.…”

Section:  mentioning

confidence: 99%

“…(5) and (6) is an important part of any method which uses this set of equations to generate the grid. In addition to the elementary method, proposed in (Thompson, et al, 1974), many researchers have proposed methods for the automatic calculation of the boundary values of control functions (Thomas & Middlecoff, 1980;Spekreijse, 1995;Steger & Sorenson, 1997;Kaul, 2003;Lee & Soni, 2004;Ashrafizadeh & Raithby, 2006;Kaul, 2010    i boundaries in Fig. 1a, the P values at internal nodes can be obtained through the following one dimensional interpolation formula (Thomas & Middlecoff, 1980):…”

Section:  mentioning

confidence: 99%

“…Therefore, using the paving layers, it is possible to generate boundary data which actually describe the boundary cell geometries or the shape of coordinate lines crossing the boundary. A simple algebraic method for generating high quality paving layers is introduced in (Ashrafizadeh & Raithby, 2006).…”

Section: Interpolantsmentioning

confidence: 99%

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