Direct Control of the Grid Point Distribution in Meshes Generated by Elliptic Equations

Thomas, P. D.; Middlecoff, Jacques

doi:10.2514/3.50801

Cited by 302 publications

(105 citation statements)

References 1 publication

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“…Interchanging dependent and independent variables for equations (19a, and b), gives: The coordinate control functions P and Q are chosen to influence the structure of the grid, [10]. The solution of these equations is obtained using Successive over Relaxation (SOR) method with relaxation factor value equal to 1.4, [11and 12].The transformed computational grid is shown in figure (2) below.…”

Section: Grid Generationmentioning

confidence: 99%

Numerical Investigation of Natural Convection Heat Transferfrom Square Cylinder in an Enclosed Enclosure Filled with Nanofluids

Alí¹,

Kahwaji²

2015

IJMECH

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Section: Grid Generationmentioning

confidence: 99%

Numerical Investigation of Natural Convection Heat Transferfrom Square Cylinder in an Enclosed Enclosure Filled with Nanofluids

Alí¹,

Kahwaji²

2015

IJMECH

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“…(5) and (6). This method is similar to the TTM as employed in (Thomas & Middlecoff, 1980) except that a multi-dimensional interpolation method is used to calculate internal values of the source functions.…”

Section: The Dd2 Methodsmentioning

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%

Alternative Methods for Generating Elliptic Grids in Finite Volume Applications

Ashrafizadeh¹,

Ebrahim²,

Jalalabadi³

2012

Finite Volume Method - Powerful Means of Engineering Design

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“…The source terms P i of Equation (1) are necessary to control the grid point distribution and several formulations [40][41][42] are used to meet grid quality measures, e.g., first cell spacing and orthogonality, cell skewness and expansion ratio. …”

Section: Discretizationmentioning

confidence: 99%

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

Mueller

Verstraete

2017

IJTPP

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Abstract:The adjoint method is considered as the most efficient approach to compute gradients with respect to an arbitrary number of design parameters. However, one major challenge of adjoint-based shape optimization methods is the integration into a computer-aided design (CAD) workflow for practical industrial cases. This paper presents an adjoint-based framework that uses a tailored shape parameterization to satisfy geometric constraints due to mechanical and manufacturing requirements while maintaining the shape in a CAD representation. The system employs a sequential quadratic programming (SQP) algorithm and in-house developed libraries for the CAD and grid generation as well as a 3D Navier-Stokes flow and adjoint solver. The developed method is applied to a multipoint optimization of a turbocharger radial turbine aiming at maximizing the total-to-static efficiency at multiple operating points while constraining the output power and the choking mass flow of the machine. The optimization converged in a few design cycles in which the total-to-static efficiency could be significantly improved over a wide operating range. Additionally, the imposed aerodynamic constraints with strict convergence tolerances are satisfied and several geometric constraints are inherently respected due to the parameterization of the turbine. In particular, radial fibered blades are used to avoid bending stresses in the turbine blades due to centrifugal forces. The methodology is a step forward towards robustness and consistency of gradient-based optimization for practical industrial cases, as it maintains the optimal shape in CAD representation. As shown in this paper, this avoids shape approximations and allows manufacturing constraints to be included.

show abstract

Direct Control of the Grid Point Distribution in Meshes Generated by Elliptic Equations

Cited by 302 publications

References 1 publication

Numerical Investigation of Natural Convection Heat Transferfrom Square Cylinder in an Enclosed Enclosure Filled with Nanofluids

Numerical Investigation of Natural Convection Heat Transferfrom Square Cylinder in an Enclosed Enclosure Filled with Nanofluids

Alternative Methods for Generating Elliptic Grids in Finite Volume Applications

CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine

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