An immersogeometric formulation for free-surface flows with application to marine engineering problems

Abstract

An immersogeometric formulation is proposed to simulate free-surface flows around structures with complex geometry. The fluid-fluid interface (air-water interface) is handled by the level set method, while the fluid-structure interface is handled through an immersogeometric approach by immersing structures into non-boundary-fitted meshes and enforcing Dirichlet boundary conditions weakly. Residual-based variational multiscale method (RBVMS) is employed to stabilize the coupled Navier-Stokes equations of incompressible flows and level set convection equation. Other level set techniques, including redistancing and mass balancing, are also incorporated into the immersed formulation. Adaptive quadrature rule is used to better capture the geometry of the immersed structure boundary by accurately integrating the intersected background elements.

A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations

“…Later, when dealing with the incompressible Navier‐Stokes equations, the time‐stepping scheme was used in a different manner: the velocity was evaluated at the intermediate time step as per the generalized‐ scheme, while the pressure was collocated at the time step t n + 1 . This choice of temporal discretization has in fact become quite popular in both CFD and FSI simulations (see, e.g., References 5‐18). In geometric multiscale modeling, this dichotomous approach to time discretization further leads to a troubling question.…”

IGA-PD Penalty-Based Coupling for Immersed Air-Blast Fluid-Structure Interaction: A Simple and Effective Solution for Fracture and Fragmentation

“…Constraining the foreground solid to the background fluid kinematics as in [7] gives the desired modularity together with strong coupling, however, the modeling of fracture and fragmentation in the immersed FSI simulations remains a challenge. While the foreground discretization such as PD can easily support discontinuous kinematic fields by locally breaking bonds between material points [11][12][13][14][15][16][17][18][19], the smooth background discretization of IGA [20][21][22][23][24][25][26][27][28] is not designed to excel in approximating discontinuous kinematics. Thus, constraining the foreground solution to its background counterpart results in an overly smooth foreground solution and, when coupled with continuum-damage (or phasefield [26,27]) approaches to model fracture and fragmentation, results in the size of damage zones that scales with that of the background mesh.…”

Industrial scale large eddy simulations (LES) with adaptive octree meshes using immersogeometric analysis

“…IMGA has been deployed by several research groups for a variety of fluid-structure interaction (FSI) simulations, including complex biomedical applications with NURBS [14,15,16,17], design optimization [18], external aerodynamics simulations with tetrahedral meshes [19,20,21,22], and moving objects [23,24]. The weak imposition of the no-slip condition has been demonstrated to be numerically very advantageous, especially for flow past complex geometries where steep gradients are produced [25,26]. However, challenges remain to practical deployment of IMGA, especially towards the goal of overnight LES.…”

“…• I -O test: Classifying the location of a point in the background mesh with respect to the object (as inside or outside the object) is a quintessential IBM ingredient. We go beyond conventional ray-tracing approaches [26,19] (which are computationally expensive) to a more efficient normal based test.…”