Topology optimization of unsteady flows using the spectral element method

We investigate the applicability of a high-order Spectral Element Method (SEM) to density based topology optimization unsteady flows in two dimensions. Direct Numerical Simulations (DNS) are conducted relying on Brinkman penalization describe presence solid within domain. The procedure uses adjoint-variable method compute gradients and checkpointing strategy reduce storage requirements. A nonlinear filtering is used both enforce minimum length scale provide smoothing across fluid–solid interface, preventing Gibbs oscillations. This has been successfully applied design channel bend an oscillating pump, demonstrates good agreement with body fitted meshes. precise pump shown depend initial material distribution. However, underlying pumping mechanism same. effect studied, revealing it be necessary regularization constraint for produce meaningful designs. combination SEM offer some unique challenges which addressed discussed, namely lack explicit boundary tracking exacerbated by interface smoothing. Nevertheless, can achieve equivalent levels precision traditional finite element methods, while requiring fewer degrees freedom. Hence, use addresses major bottlenecks associated optimizing flows: computation cost data storage.