Abstract
A least-squares spectral collocation scheme is combined with the overlapping Schwarz method. The methods are succesfully applied to the incompressible Navier–Stokes equations. The collocation conditions and the interface conditions lead to an overdetermined system which can be efficiently solved by least-squares. The solution technique will only involve symmetric positive definite linear systems. The overlapping Schwarz method is used for the iterative solution. For parallel implementation the subproblems are solved in a checkerboard manner. Our approach is successfully applied to the lid-driven cavity flow problem. Only a few Schwarz iterations are necessary in each time step. Numerical simulations confirm the high accuracy of our spectral least-squares scheme.
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Heinrichs, W. Least-squares spectral collocation with the overlapping Schwarz method for the incompressible Navier–Stokes equations. Numer Algor 43, 61–73 (2006). https://doi.org/10.1007/s11075-006-9039-1
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DOI: https://doi.org/10.1007/s11075-006-9039-1