Improved volume conservation in the computation of flows with immersed elastic boundaries

This paper introduces a recipe for the construction of a finite-difference divergence operator the coefficients of which are completely determined once an interpolation scheme has been chosen. Substitution of this divergence operator for the previously used divergence based on central differences makes a dramatic improvement in the overall volume conservation that is observed in an immersed-boundary computation. This improvement is particularly important for computations in which an elastic boundary separates chambers containing fluid at substantially different pressures, a situation which is prominent in cardiac fluid dynamics during the contraction of the ventricles.