An explicit and non-iterative immersed boundary method for incompressible flows with scalar fields*

Incompressible flows with scalar fields are very common in natural and engineering applications, and are often accompanied by complex motion and deformation boundary, such as fluid-structure interaction, finite-size particle flows, and bubbly flow. To solve such problems, a numerical method based on the moving least squares immersed boundary method is proposed. We reveal that the boundary error of the baseline method follows a narrow peak distribution, and propose an explicit and non-iterative correction method. This method can be used to correct the volume force of velocity field and scalar field, including the Dirichlet and Neumann boundary conditions. Validation calculations are performed for the flows over the stationary sphere and the flexible flag, the buoyant sphere and the mixed convection around an iso-heat-flux rotating sphere. The results demonstrate that the proposed method can achieve low boundary error similar to the iterative method, but with less computing time. This method can be further combined with the iterative methods to achieve smaller error and may also be applied to other types of diffusion-type immersed boundary methods.