Accurate iteration-free mixed-stabilised formulation for laminar incompressible Navier-Stokes: Applications to fluid-structure interaction
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Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to solve the nonlinearity in the convection term. One fundamental issue with this approach is the computational cost incurred in the Newton-Raphson iterations at every load/time step. In this paper, we present an iteration-free mixed-stabilised finite element formulation for incompressible Navier-Stokes that preserves second-order temporal accuracy for both velocity and pressure fields. We prove the second-order temporal accuracy using an example with a manufactured solution. We then illustrate the accuracy and the computational benefits of the proposed scheme by studying the benchmark example of flow past a fixed circular cylinder and then using two benchmark examples in fluid-flexible structure interaction.
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