A COMPARITIVE STUDY OF TIME ADVANCEMENT METHODS FOR SOLVING NAVIER-STOKES EQUATIONS

By T.K. Sengupta and A. Dipankar

A qualitative and quantitative study is made for choosing time advancement strategies for solving time dependent equations accurately. A single step, low order Euler time integration method is compared with Adam-Bashford, a second order accurate time integration strategy for the solution of one-dimensional wave equation. With the help of the exact solution, it is shown that the presence of computational mode in Adam-Bashford scheme leads to erroneous results, if the solution contains high-frequency components. This is tested for the solution of incompressible Navier-Stokes equation for uniform flow past a rapidly rotating circular cylinder. This flow suffers intermittent temporal instabilities implying presence of high frequencies. Such instabilities have been noted earlier in experiments and high accuracy computations for similar flow parameters. This test problem shows that second order Adam-Bashford time integration is not suitable for DNS.