Accurate computation of surface stresses and forces with immersed boundary methods
Abstract
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them illsuited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluidstructure interaction problems, to obtain smooth and convergent stress distributions on the surface. To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose illposedness is the source of spurious oscillations in the stresses. We also demonstrate that for sufficiently smooth delta functions, the oscillations may be filtered out to obtain physically accurate surface stresses. The filtering is applied as a postprocessing procedure, so that the convergence of the velocity field is unaffected. We demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 2016
 DOI:
 10.1016/j.jcp.2016.06.014
 arXiv:
 arXiv:1603.02306
 Bibcode:
 2016JCoPh.321..860G
 Keywords:

 Immersed boundary method;
 Nonphysical surface forces;
 Integral equation of the first kind;
 Regularization;
 Fluidstructure interaction;
 Physics  Fluid Dynamics;
 Physics  Computational Physics
 EPrint:
 doi:10.1016/j.jcp.2016.06.014