| Abstract: |
| In the talk we report novel first- and second-order decoupled schemes for the Navier-Stokes equations based on the penalty method and the sequential regularization method (SRM), respectively. These schemes do not require the boundary condition on the pressure and thus preserve the original velocity boundary conditions. By using the idea of the scalar auxiliary variable (SAV), the nonlinear terms of these schemes are treated explicitly. We also carefully reformulated the Navier-Stokes equations to ensure convergence of the proposed scheme without any restriction on the time step. At each time step it is only necessary to solve elliptic equations with constant coefficients. An unconditional (without time step constraints) global optimal error estimate is shown. Furthermore, to more accurately approximate the incompressibility constraint without introducing extra stiffness into the system, a sequential regularization SAV scheme is developed, and is error estimate is provided as well. Finally, we compare our proposed schemes with the classic linearized projection scheme to demonstrate its accuracy and efficiency, and discuss the application of the idea to phase-field models. This is a joint work with Z Wang. |
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