An explicit and non-iterative moving-least-squares immersed-boundary method with low boundary velocity error

Abstract

In this work, based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary. For boundary with simple geometry, we theoretically analyze the error between the desired volume force at boundary and the actual force given by the original method. The ratio between the two forces is very close to a constant and exhibits a very narrow distribution. A spatially uniform coefficient is then introduced to correct the force and can be fixed by the least-square method over all boundary markers. Such method is explicit and non-iterative, and is easy to implement into the existing scheme. Several test cases have been simulated with stationary and moving boundaries. Our new method can reduce the residual boundary velocity to the level comparable to that given by the iterative method, but requires much less computing time. Preliminary test suggests that the current method is also effective for nonuniform Eulerian grid. Moreover, the new method can be readily combined with the iterative method and further reduces the residual boundary velocity.