Aglobal time integration approachfor realistic unsteady flow computations

A novel time integration approach is explored for unsteady flow computations. The time dependent solutions are blocked in time and one solves for all solutions within a block simultaneously. The time discretization within a block is based on the summation-by-parts (SBP) technique in time combined with the simultaneous-approximation-term (SAT) technique for imposing the initial condition. The approach is implicit, unconditionally stable and can be made arbitrary accurate in time. The implicit system is solved by solving by dal time stepping technique. The novel approach has been implemented in a flow solver for unstructured grids and applied to an unsteady flow problem with vortex shedding over a cylinder. Three time integration approaches being 2^nd, 3^rd and 4^th order accurate in time are evaluated and compared to the conventional 2^nd backward difference (BDF2) method. The order of accuracies are verified for all approaches. The efficiencies of the approaches reveal that the 3^rd and 4^th accurate method is the most efficient one and comparable to the efficiency of the BDF2 scheme. The influence of the size of the time blocks is small in terms of overall accuracy but smaller blocks are somewhat more efficient. There is a large potential for improvements from alternative initialization of time blocks, even higher order operators and non-constant time steps.