The Adaptation of Two-Dimensional Multiblock Structured Grids Using a PDE-Based Method

  • D. Catherall
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 44)


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’.

In the work described here a new, but related, method, termed the LPE method, is introduced to overcome this limitation. In this approach each grid equation is formed from
  1. 1.

    an inverted Laplace equation (the L in LPE) which, if used in isolation, maximises smoothness and orthogonality.

  2. 2.

    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.

  3. 3.

    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.

Control is effected through choosing the relative weights to be placed on these three constituents of the grid equations. Grid control in the region of trailing edges is obtained separately through the use of source terms placed there.

Other features of the method described here include enforced grid orthogonality at grid boundaries and implementation on multiblock structured grids.


Mach Number Grid Line Flow Solver Inviscid Flow Solution Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • D. Catherall
    • 1
  1. 1.Defence Research Agency Aerodynamics DepartmentRoyal Aerospace EstablishmentFarnborough Hants.UK

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