A Cartesian-octree adaptive front-tracking solver for immersed biological capsules in large complex domains

TL;DR

This paper introduces an open-source adaptive front-tracking solver for biological capsules in viscous flows, combining Lagrangian membrane modeling with an octree adaptive grid for accurate and robust simulations in complex geometries.

Contribution

The novel solver integrates membrane mechanics with an octree adaptive grid and immersed boundary method, enabling accurate simulations of biological capsules in complex, large-scale domains.

Findings

Validated against Boundary Integral Method in Stokes flow

Demonstrated robustness in extreme membrane deformation

Capable of simulating inertial flows in complex geometries

Abstract

We present an open-source adaptive front-tracking solver for biological capsules in viscous flows. The membrane elastic and bending forces are solved on a Lagrangian triangulation using a linear Finite Element Method and a paraboloid fitting method. The fluid flow is solved on an octree adaptive grid using the open-source platform Basilisk. The Lagrangian and Eulerian grids communicate using an Immersed Boundary Method by means of Peskin-like regularized Dirac delta functions. We demonstrate the accuracy of our solver with extensive validations: in Stokes conditions against the Boundary Integral Method, and in the presence of inertia against similar (but not adaptive) front-tracking solvers. Excellent qualitative and quantitative agreements are shown. We then demonstrate the robustness of the present solver in a challenging case of extreme membrane deformation, and illustrate its capability to simulate inertial capsule-laden flows in complex STL-defined geometries, opening the door for bioengineering applications featuring large three-dimensional channel structures. The source code and all the test cases presented in this paper are freely available.