Current calculations of complex unsteady flows are prohibitively expensive for use in real engineering applications. Typical flow solvers for unsteady integration employ a fully implicit time stepping scheme, in which the equations are solved by an inner iteration. In order to achieve convergence within each physical time step, a substantial number of pseudo-time steps (typically between 30-100...

In this work, we will analyze a class of large time-stepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerica...

Abstract. We consider fully discrete finite element approximations of a distributed optimal control problem, constrained by the evolutionary Stokes equations. Conforming finite element methods for spatial discretization combined with discontinuous time-stepping Galerkin schemes are being used for the space-time discretization. Error estimates are proved under weak regularity hypotheses for the ...

This paper presents the formulation of a dual time stepping procedure to solve the equations of fully implicit Runge–Kutta schemes. In particular themethod is applied toGauss and Radau 2A schemes with either two or three stages. The schemes are tested for unsteady flows over a pitching airfoil modeled by both the Euler and the unsteady Reynolds averaged Navier Stokes equations. It is concluded ...

[1] Problems associated with shear zone development in the lithosphere involve features of widely different time scales, since the gradual buildup of stress leads to rapid and localized shear instability. These phenomena have a large stiffness in time domain and cannot be solved efficiently by a single time-integration scheme. This conundrum has forced us to use an adaptive time-stepping scheme...