| Popis: |
We propose new high order versions of the collocations and least squares (CLS) method for 2D stationary Navier-Stokes equations. In these versions, components of the solution are sought in the form of piecewise-polynomial functions. Computational domain is covered by a grid with rectangular cells. Velocity components are approximated by polynomials of degree m v at most in both spatial directions in each cell of the grid. Polynomials for velocity v are chosen so that the approximate solution exactly satisfies continuity equation v = 0 inside each cell. Pressure is approximated by polynomials of degree m p at most respectively. New versions of the CLS method were implemented on regular and nonregular grids with rectangular cells here. The method was verified on a problem with analytical exact solution and benchmark lid-driven cavity flow problem. Computational results for the latter one coincide with highly accurate solutions obtained by other researchers (Barragy E., Botella O., Erturk E., Shapeev A., etc.) with the accuracy 10-7 ~10-8 for Re = 1000. |
