Navier-Stokes equations as differential-algebraic equations and its numerical solution with sequential regularization method


Differential- algebraic equations (DAEs) play an important role in mathematical models. In this study, after discussing some difficulties involved in numerical solution to differential- algebraic equations we use sequential regularization method (SRM) for solving Hessenberg index-2 and index-3 DAEs. Then Navier-Stokes equations that have extensively used in fluid dynamics are considered as differential- algebraic equations and are solved with SRM. In contrast to the linear method for solving Navier-Stokes, initial values for pressure are not required and the problems are solved with less stiffness. In this paper we compare the above mentioned methods with predicted sequential regularizations method (PSRM) which significantly improves computational time over the SRM. Finally numerical results are given.