  This paper presents a one-sided immersed boundary (IB) method using kernel
functions constructed via a moving least squares (MLS) method. The resulting
kernels effectively couple structural degrees of freedom to fluid variables on
only one side of the fluid-structure interface. This reduces spurious feedback
forcing and internal flows that are typically observed in IB models that use
isotropic kernel functions to couple the structure to fluid degrees of freedom
on both sides of the interface. The method developed here extends the original
MLS methodology introduced by Vanella and Balaras (J Comput Phys, 2009). Prior
IB/MLS methods have used isotropic kernel functions that coupled fluid
variables on both sides of the boundary to the interfacial degrees of freedom.
The original IB/MLS approach converts the cubic spline weights typically
employed in MLS reconstruction into an IB kernel function that satisfies
particular discrete moment conditions. This paper shows that the same approach
can be used to construct one-sided kernel functions (kernel functions are
referred to as generating functions in the MLS literature). We also examine the
performance of the new approach for a family of kernel functions introduced by
Peskin. It is demonstrated that the one-sided MLS construction tends to
generate non-monotone interpolation kernels with large over- and undershoots.
We present two simple weight shifting strategies to construct generating
functions that are positive and monotone, which enhances the stability of the
resulting IB methodology. Benchmark cases are used to test the order of
accuracy and verify the one-sided IB/MLS simulations in both two and three
spatial dimensions. This new IB/MLS method is also used to simulate flow over
the Ahmed car model, which highlights the applicability of this methodology for
modeling complex engineering flows.
