Multi-dimensional limiting process for three-dimensional flow physics analyses

Yoon, Sung-Hwan; Kim, Chongam; Kim, Kyu Hong

doi:10.1016/j.jcp.2008.02.012

Cited by 78 publications

(56 citation statements)

References 42 publications

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“…As the same time, multi-dimensional limiting process (MLP) [4][5][6] is also proposed to achieve high-order spatial accuracy and to incorporate multi-dimensional effect. Exploiting these numerical schemes, reliable two-and three-dimensional internal/external flow analyses can be carried out with various grid systems.…”

Section: Numerical Schemes For Flow Analysismentioning

confidence: 99%

“…By extending the one-dimensional monotonic condition to 2-D and 3-D flows, the multi-dimensional limiting condition is proposed, and with this limiting condition, the multidimensional limiting process (MLP) [4][5][6] can be formulated. The starting point is the observation that the dimensional splitting extension does not possess any information on property distribution at cell vertex points, whose information is essential when property gradient is not aligned with local grid lines.…”

Section: Multi-dimensional Limiting Processmentioning

confidence: 99%

“…For detailed explanation, Fig. 1 shows the computed results of shock-vortex interaction [4][5][6] . Compared to conventional limiting, MLP can control oscillations across the shock discontinuity and capture local flow structure in detail.…”

Section: Multi-dimensional Limiting Processmentioning

confidence: 99%

“…Both RoeM and AUSMPW+ schemes are among the recently developed advanced numerical fluxes for gas dynamics. In addition, to achieve high-order spatial accuracy by incorporating multi-dimensional flow physics, multi-dimensional limiting process (MLP) are discussed in 2-D and 3-D setting [4][5][6] . The sensitivity analysis method commonly used can be summarised by four techniques, (i) finite difference method (FDM) 7 , (ii) direct differentiation (DD) 8 , (iii) complex step derivative 9 , and (iv) continuous/discrete adjoint variables 7,10 .…”

Section: Introductionmentioning

confidence: 99%

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Computational Elements for High-fidelity Aerodynamic Analysis and Design Optimisation

Kim

2010

DSJ

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The study reviews the role of computational fluid dynamics (CFD) in aerodynamic shape optimisation, and discusses some of the efficient design methodologies. The article in the first part, numerical schemes required for high-fidelity aerodynamic flow analysis are discussed. To accurately resolve high-speed flow physics, high-fidelity shock-stable schemes as well as intelligent limiting strategy mimicking multi-dimensional flow physics are essential. Exploiting these numerical schemes, some applications for 3-D internal/external flow analyses were carried out with various grid systems which enable the treatment of complex geometries. In the second part, depending on the number of design variables and the way to obtain sensitivities or design points, several global and local optimisation methods for aerodynamic shape optimisation are discussed. To avoid the problem that solutions of gradient-based optimisation method, (GBOM) are often trapped in local optimum, remedy by combining GBOM with global optimum strategy, such as surrogate models and genetic algorithm (GA) has been examined. As an efficient grid deformation tool, grid deformation technique using NURBS function is discussed. Lastly, some 3-D examples for aerodynamic shape optimisation works based on the proposed design methodology are presented.

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Section: Numerical Schemes For Flow Analysismentioning

confidence: 99%

Section: Multi-dimensional Limiting Processmentioning

confidence: 99%

Section: Multi-dimensional Limiting Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational Elements for High-fidelity Aerodynamic Analysis and Design Optimisation

Kim

2010

DSJ

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“…For example, Batten et al [6] construct several trial gradients, limit each using a scalar limiter, and then choose the one with the largest norm. Park et al [28] extended the multi-dimensional limiting process (MLP) introduced in [24,33] from structured to unstructured meshes, and use an enlarged stencil in the limiting process.…”

mentioning

confidence: 99%

Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes

May¹,

Berger²

2013

SIAM J. Sci. Comput.

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Abstract. In this paper we develop a new limiter for linear reconstruction on non-coordinatealigned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two-dimensional and linearity preserving. It separately limits the x and y components of the gradient, as opposed to a scalar limiter which limits all components simultaneously with one scalar. The limiter is based on solving a tiny linear program (LP) on each cell, using a very efficient version of the simplex method. A variety of computational results on triangular and embedded boundary meshes are presented. They demonstrate that the LP limiter successfully removes oscillations and significantly increases solution accuracy compared to a scalar limiter.

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Influence of spatial discretization and unsteadiness on the simulation of rocket combustors

Lempke

Keller

Gerlinger

2015

Numerical Methods in Fluids

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Summary This paper investigates some important numerical aspects for the simulation of model rocket combustors. Precisely, (1) a new high‐order discretization technique (multi‐dimensional limiting process (MLP), low diffusion, and MLPld) is presented and compared with conventional second‐order schemes with different flux limiters. (2) Time accurate unsteady Reynolds‐averaged Navier–Stokes (RANS) simulations are performed to assess possible improvements in comparison with steady‐state RANS simulations. (3) Fully 3D simulations of an axisymmetric rocket combustor are compared with 2D axisymmetric ones. All studies are based on the Penn State preburner combustor experiment, which uses gaseous oxygen and hydrogen. This comprehensive study offers unique insight into how the mentioned numerical influence factors change the flow field, flame, and wall heat fluxes in the model rocket combustor. Because wall heat fluxes are known from the experiment only, numerical results are compared with LES of other authors, too. It will be shown that the high‐order spatial discretization significantly improves the agreement with measured wall heat fluxes at low additional computational cost. In general the transition from simple to more complex numerical approaches steadily improves the qualitative agreement between simulation and experiment. Copyright © 2015 John Wiley & Sons, Ltd.

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Multi-dimensional limiting process for three-dimensional flow physics analyses

Cited by 78 publications

References 42 publications

Computational Elements for High-fidelity Aerodynamic Analysis and Design Optimisation

Computational Elements for High-fidelity Aerodynamic Analysis and Design Optimisation

Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes

Influence of spatial discretization and unsteadiness on the simulation of rocket combustors

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