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

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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this study, a new technique is proposed to improve the calculation of the volume force representing the body boundary based on the moving-least-squares immersed boundary method. The error between the desired volume force and the actual force given by the original method is theoretically analyzed for boundaries with simple geometry. A spatially uniform coefficient is introduced to correct the force, and it can be determined by the least-square method over all boundary markers. The new method shows promising results in reducing boundary velocity residual and can be combined with the iterative method for further improvement.