Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations

Steger, J. L.; Sorenson, Reese L.

doi:10.1016/0021-9991(79)90165-7

Cited by 222 publications

(65 citation statements)

References 6 publications

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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%

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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.

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Section: Discretizationmentioning

confidence: 99%

“…Although the computational cost to compute gradients with the complex-step method is proportional to the number of design parameters, it is still considered reasonable given the limited number of design parameters used in this study (40) and the relatively fast grid generation process.…”

Section: Multigrid Cyclementioning

confidence: 99%

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

Mueller

Verstraete

2017

IJTPP

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“…A variable volumetric force is used such that a constant mass flux is maintained and the bulk Reynolds number based on the bulk velocity at the inlet and hill height is Re b = 10595. An elliptic grid generation technique [39] is used to generate a nearly orthogonal curvilinear grid in the x-y plane with clustering of the grid near the upper and lower walls to resolve the boundary layers. The grid in the 8 Taylor & Francis and I.T.…”

Section: Periodic Hill Flowmentioning

confidence: 99%

Large eddy simulation of channel flow with and without periodic constrictions using the explicit algebraic subgrid-scale model

Rasam

Wallin

Brethouwer

et al. 2014

Journal of Turbulence

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PostprintThis is the accepted version of a paper published in Journal of turbulence. This paper has been peerreviewed but does not include the final publisher proof-corrections or journal pagination. Citation for the original published paper (version of record):Rasam, A., Wallin, S., Brethouwer, G., Johansson, A V. (2014) Large eddy simulation of channel flow with and without periodic constrictions using the explicit algebraic subgrid-scale model. Vol. 15, No. 11, 2014, 1-24 Large eddy simulation of channel flow with and without periodic constrictions using the explicit algebraic subgrid-scale model & Fluids, vol. 38, 2009, pp.433-457) using the DSM. Results show that the mean velocity profiles, the friction and pressure coefficients, the length and shape of the recirculation bubble, as well as the Reynolds stresses are considerably better predicted by the EASSM than the DSM and the no SGS model simulations. It was also observed that in some parts of the domain the resolved strain-rate and SGS shear stress have the same sign. The DSM cannot produce a correct SGS stress in this case, in contrast to the EASSM. Journal of turbulence,

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“…Computational grids were generated using an interactive program called TIGGERC [ 151 in conjunction with interior grid restretching using an elliptic partial differential equation (PDE) solver [16]. The elliptic PDE solver forces grid orthogonality at solid boundaries, and allows user control of the grid spacing normal and adjacent to the boundaries, and of the stretching away from the boundaries.…”

Section: Computational Detailsmentioning

confidence: 99%

Rapid numerical simulation of viscous axisymmetric flow fields

Tweedt

Chima

1996

34th Aerospace Sciences Meeting and Exhibit

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A two-dimensional Navier-Stokes code has been developed for rapid numerical simulation of axisymmebic flow fields, including flow fields with an azimuthal velocity component. The azimuthal-invariant Navier-Stokes equations in a cylindrical coordinate system are mapped to a general body-fitted coordinate system, with the streamwise viscous terms then neglected by applying the thinlayer approximation. Turbulence effects are modeled using an algebraic model, typically the Baldwin-Lomax turbulence model, although a modified Cebeci-Smith model can also be used. The equations are discretized using central finite differences and solved using a multistage Runge-Kutta algorithm with a spatially-varying time step and implicit residual smoothing.Results are presented for calculations of supersonic flow over a waisted body-of-revolution, transonic flow through a normal shock wave in a straight circular duct of constant cross-sectional area, swirling supersonic (inviscid) flow through a strong shock in a straight radial duct, and swirling subsonic flow in an annular-to-circular diffuser duct. Comparisons between computed and experimental results a r e in fair to good agreement, demonstrating that the viscous code can be a useful tool for practical engineering design and analysis work.

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Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations

Cited by 222 publications

References 6 publications

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

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

Large eddy simulation of channel flow with and without periodic constrictions using the explicit algebraic subgrid-scale model

Rapid numerical simulation of viscous axisymmetric flow fields

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