The Navier-Stokes equations describe the flow of fluids and thus have a lot of applications, for instance in modelling the weather and oceans, and in designing aircraft and cars. It is therefore important that numerical solutions can be found efficiently. There are methods that c
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The Navier-Stokes equations describe the flow of fluids and thus have a lot of applications, for instance in modelling the weather and oceans, and in designing aircraft and cars. It is therefore important that numerical solutions can be found efficiently. There are methods that can be used when numerically solving the equations, namely the Newton-Raphson method and the Picard iteration, but these methods can fail when the fluid has certain properties. Anderson acceleration is a numerical method that can improve the rate at which the Picard iteration converges towards the solution.
In this paper, Anderson acceleration is first implemented for problems in one dimension. It is then extended to problems in multiple dimensions and applied to the Navier-Stokes equations. Its performance is compared to that of the Newton-Raphson method and the Picard iteration. From this, it follows that Anderson acceleration can indeed improve the convergence rate of Picard. Furthermore, the method can find solutions in situations where the Newton-Raphson method and the Picard iteration do not.
