The Adaptation of Two-Dimensional Multiblock Structured Grids Using a PDE-Based Method
In previous work it has been shown that solution-adapted grids may be obtained by solving Poisson equations for the node ordinates with the control functions evaluated from a solution obtained on the original grid. However, this can lead to a situation where both the elliptic terms in the grid equations, and the equidistribution mechanism implied in the evaluation of the control functions, attract grid nodes to certain regions, so producing an ‘overkill’.
an inverted Laplace equation (the L in LPE) which, if used in isolation, maximises smoothness and orthogonality.
an inverted Poisson equation (the P in LPE) with control functions evaluated from the original grid — if used in isolation the original grid is regenerated.
an Equidistribution equation (the E in LPE) which, if used in isolation, distributes nodes along each grid line so that node separations are inversely proportional to the local value of a sensor function formed from solution gradients.
Other features of the method described here include enforced grid orthogonality at grid boundaries and implementation on multiblock structured grids.
KeywordsMach Number Grid Line Flow Solver Inviscid Flow Solution Gradient
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