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. In a first time, we theoretically analyse the truncation error of the scheme and perform a linear stability analysis of it. Then some numerical experiments over simple test-cases are presented. Finally, the capability and accuracy of this new scheme is outlined by the analisys of a complex unsteady flow in a 2-D model of a piston engine.