A second order defect correction scheme for unsteady problems

Using the defect correction method (DeC), we propose an implicit scheme that is second order accurate both in time and space, but that uses only first order jacobian. We start a theoretical analysis of the truncation error of the scheme and then perform a linear stability analysis of it. We present some numerical experiments over simple test-cases. Finally, the capability and accuracy of this new scheme is outlined by the analysis of a complex unsteady flow in a 2-D model of a piston engine.