A novel mass and momentum conserving immersed boundary method based on volume-filtering.

We present a novel approach towards solving for complex boundaries within a flow using the

immersed boundaries method in a conservative manner without the need for body-fitting meshes.

This method uses the volume-filtering approach by taking the boundary conditions at the

interfaces and turning them into body forces that apply to the right-hand side of the mass and

momentum equations. This rigorous mathematical and physical volume-filtering framework, allows to

explicitly express the immersed boundary forcing terms, without assuming any

particular discretization scheme. The derivation of this method is based on selecting a filter

kernel that is symmetric in nature, and one that integrates to unity. The usage of the filter kernel

creates new filtered equations, similar in style to the LES approach. These equations include the

body forces and the sub-filter scale terms which are closed using various methods specific to the

term. To show the accuracy of the method, 3 canonical test cases are run: (1) static cylinder at

Reynolds number of 100, (2) oscillating cylinder at Reynolds number of

100, and (3) flow past a sphere with increasing Reynolds number. The results are compared with previous experiments or

simulations with body-fitted meshes. The accuracy of different filter kernels (Box, triangle,

cosine, Roma-Peskin and parabolic) at different filter widths compared to the grid spacing are

tested.