A Variational Form of the Winslow Grid Generator

Charakhch’yan, A. A.; Ivanenko, S. A.

doi:10.1006/jcph.1997.5750

Cited by 53 publications

(55 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider, in particular, methods based on or derived from the quasi-conformal mappings [2], [3] and on harmonic mappings [1], [4], [6], [9]. In this approach the computational grids are constructed via the minimization of a discrete counterpart of the Dirichlet functional and its generalizations.…”

Section: Introductionmentioning

confidence: 99%

“…In [8], [9] it was shown that some discrete approximations to the generalized Dirichlet functional have a barrier on the boundary of the set of grids consisting of convex quadrilateral cells.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of quality measure t, "dimensionless" in a sense that 0 < t < 1 , it is possible to consider the parameterized feasible set T (t), consisting of grids where the quality of each cell is above a threshold value t. Then .F(O) denotes the set of non-degenerate grids and .F(l) is the grid consisting of "ideal" cells. Typically in barrier grid generation methods [8], [9] and in barrier construction of nondegenerate mappings [14], [19], [18], the barrier is constructed on 9 J7(0). The basic idea of the present work is to construct the barrier on d T (t) and to "contract" it which means to find the grid with the maximum possible quality measure t = t max.…”

Section: Introductionmentioning

confidence: 99%

“…It is useful to analyze the properties of the function f(A) defined by (9). To this end let us consider the auxiliary minimization problem…”

Section: Introducing the New Notationmentioning

confidence: 99%

“…Here Vç denotes the gradient operator in logical coordinates, = (ff^* • • • > | | 1)T and <j>(A) is defined by (9).…”

Section: Introducing the New Notationmentioning

confidence: 99%

See 4 more Smart Citations

Barrier variational generation of quasi‐isometric grids

Гаранжа

2001

Numerical Linear Algebra App

View full text Add to dashboard Cite

A b str a c tT he grid generation m ethod based on th e m inim ization of th e discrete barrier functional w ith feasible set consisting of quasi-isom etric grids is suggested. T he deviation from isom etry for given grid connectivity an d fixed boundary nodes is m inim ized via th e contraction of th e feasible set into small vicinity of th e optim al grid. Form ulation of functional w ith given m etrics in b o th physical and logical spaces allows to consider th e adaptive grid generation in term s of quasi isom etric grids and cover m any practical applications. T he fast an d reliable procedure for finding feasible solution based on th e penalty-like reform ulation of barrier functional and th e continuation technique is described. T he relations between different barrier approxim ations to quasi-isom etric functional in 2-D and 3-D cases are investigated. N um erical experim ents have confirm ed th a t th e suggested functional allows to obtain high quality grids.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It is useful to analyze the properties of the function f(A) defined by (9). To this end let us consider the auxiliary minimization problem…”

Section: Introducing the New Notationmentioning

confidence: 99%

“…Here Vç denotes the gradient operator in logical coordinates, = (ff^* • • • > | | 1)T and <j>(A) is defined by (9).…”

Section: Introducing the New Notationmentioning

confidence: 99%

See 3 more Smart Citations

Barrier variational generation of quasi‐isometric grids

Гаранжа

2001

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

Application of moving adaptive grids for numerical solution of 2D nonstationary problems in gas dynamics

Ivanenko

Azarenok

2002

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYSolution-adaptive grid generation procedure is coupled with the Godunov-type solver of the secondorder accuracy. Dynamically adaptive grids, clustered to singularities, allow to increase the accuracy of numerical solution. The theory of harmonic maps is used as a theoretical framework for grid generation. The problem of constructing harmonic coordinates on the surface of the graph of control function is formulated. The projection of these coordinates onto a physical domain produces an adaptive-harmonic structured grid. A variational grid generator which can be used also in the case of unstructured grids with adaptation to a vector-function is described in detail. The discrete functional has an inÿnite barrier on the boundary of the set of grids with all convex cells and this guarantees unfolded grid generation at every time step. Results of test computations are presented.

show abstract