Design of DIRK schemes for solving the Navier-Stokes equations
In this note new diagonal-implicit Runge-Kutta methods for semi-explicit PDAEs of index 2 are presented. These solvers are stiffly accurate, of order 3 for the ODE-variables and of order 2 for the algebraic variables. They have three and four internal stages and automatic steplength control by the help of embedding is possible. The methods with four internal stages have a stiffly accurate embedded method of order 2 for all variables. The methods are applied on the incompressible Navier-Stokes equations and compared with other DIRK-methods.
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