LINEAR WAVE PROPAGATION ON AN ADAPTIVE QUAD-TREE CUT-CELL GRID

Title:

LINEAR WAVE PROPAGATION ON AN ADAPTIVE QUAD-TREE CUT-CELL GRID

DOI No:

10.1142/9789812701916_0067

Source:

COASTAL ENGINEERING 2004 (pp 842-854)

Author(s):

RODOLFO SILVA
Instituto de Ingeniería, Universidad Nacional Autónoma de México., Cd. Universitaria. Apdo. Postal 70-472. 04510 D.F., México
ALISTAIR G.L. BORTHWICK
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, U.K.
EDGAR G. MENDOZA
Instituto de Ingeniería, Universidad Nacional Autónoma de México., Cd. Universitaria. Apdo. Postal 70-472. 04510 D.F., México

Abstract:

A new adaptive quad-tree cut-cell linear wave model is presented for evaluating wave transformation over an uneven bed. The mathematical model is based on a modified version of the harmonic mild-slope equation. To account for energy losses from breaking and bottom friction, the model is altered to incorporate an energy dissipation term. Boundaries are assumed to be open, partially reflecting, or fully absorbing through the second-order parabolic approximation. It is assumed that the depths at the lateral boundaries may change solely in the landward-direction. In contrast to traditional quad-tree grid generation techniques, the main advantages of the present methodology are that rectangular domains are modelled without any distortion of the cell dimensions. The discretized equations are solved efficiently using an inexpensive banded solver because the matrix is not very sparse, due to the cell numbering system. The cut-cell technique used here to represent the solid boundaries incurs almost no extra computational cost. At boundaries, the model has fewer restrictions associated with wave obliqueness than other mild-slope equation models, and does not require absorbing sponge layers. The model has been validated and the numerical predictions are in excellent agreement with the analytical solutions.

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