Three-dimensional adaptive grid method

Abstract

A three-dimensional solution adaptive grid scheme suitable for complex fluid flows is described. This method, using tension and torsion spring analogies, was previously developed and successfully applied for twodimensional flows. In the present work, a collection of three-dimensional flowfields is used to demonstrate the feasibility and versatility of this concept to include an added dimension. Flowfields considered include: 1) supersonic flow past an aerodynamic afterbody with a propulsive jet at incidence to the freestream, 2) supersonic flow past a blunt fin mounted on a solid wall, and 3) supersonic flow over a bump. In addition to generating three-dimensional solution-adapted grids, the method can also be used effectively as an initial grid generator. The utility of the method lies in: 1) optimum distribution of discrete grid points, 2) improvement of accuracy, 3) improved computational efficiency, 4) minimization of data-base sizes, and 5) simplified three-dimensional grid generation. IntroductionA N important subject to study in computational fluid ./JLdynamics is solution adaptive grid methods, due to their potential for improving the efficiency and accuracy of numerical methods. The use of adaptive grids can be expected to help minimize computer memory and speed requirements, particularly for three-dimensional flowfield computations.Many solution adaptive grid methods have been proposed and are well reviewed by both Anderson 1 and Thompson. 2 One of the most popular of these methods is based on an equidistribution concept, 35 i.e., redistribution of grid points such that a positive weighting function, w/, is equally distributed over a coordinate line:

A dynamic adaptive grid MPDATA scheme: application to the computational solution of atmospheric tracer transport problems

“…Another, similar technique by Nakahashi and Deiwert (1986), determines inter-nodal equations as if there were tension springs between the nodes and torsional springs at the nodes. The tension springs control the grid clustering and the torsional springs gives the method of controlling the grid orthog onality.…”

Aerodynamic analysis of flapping foils using volume grid deformation code

“…A Laplacian interpolation [3] and a local mesh adaptation [4] are also used to deform meshes in the same category. A spring analogy that uses tension and torsion springs based on the equation of continuum mechanics has been frequently used as an elasticitybased approach [5][6][7]. The spring analogy, however, is known to cause grid irregularity, and subsequently techniques for improving robustness of the grid regularity need to be developed.…”

Considerations on the spring analogy

“…To give a few examples, the spring analogy is used for free surface problems by Slikkeveer et al [2], store separation problems by Hassan et al [3], forced vibration and fluid -structure interaction problems by Blom and Leyland [4], and aeroelastic calculations by Farhat et al [5] and Piperno [6]. The spring analogy is also suitable for structured meshes as is, for example, shown by Nakahashi and Deiwert [7], who used it for mesh adaptation.…”