Over the past decades, the pursuit of efficient and accurate numerical methods for modeling fluid-structure interaction (FSI) problems arising in materials science and biological applications is at the forefront of modern computational science and engineering. In this talk, I will present recent advances in the numerical methods for FSI to achieve improved accuracy and computational efficiency. The first part of the talk will focus on improving the volume conservation of the Immersed Boundary Method for modeling elastic structures moving and deforming in a fluid.

In the second part of the talk, I will present a fluctuating boundary integral method for simulating Brownian suspension of rigid particles of complex shapes. I will demonstrate how to efficiently and accurately generate, together, both the deterministic component of the particle linear and angular velocities, as well as the stochastic Brownian displacements with (near) linear-scaling as the number of particles increases.