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We present an enhanced immersed interface method for simulating incompressible fluid flows in thin gaps between closely spaced immersed boundaries. This regime, common in engineered structures such as including tribological interfaces and…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Writing high performance solvers for engineering applications is a delicate task. These codes are often developed on an application to application basis, highly optimized to solve a certain problem. Here, we present our work on developing a…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid…
A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…
Immersed boundary methods (IBMs) facilitate the simulation of flows around stationary, moving, and deforming bodies on Cartesian grids. However, extending these simulations to the large grid sizes required for realistic flow problems…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
We extend the shifted boundary method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids.…
We present an efficient implementation for running three-dimensional numerical simulations of fluid-structure interaction problems on single GPUs, based on Nvidia CUDA through Numba and Python. The incompressible flow around moving bodies…
High-fidelity simulations of unsteady fluid flow are now possible with advancements in high-performance computing hardware and software frameworks. Since computational fluid dynamics (CFD) computations are dominated by linear algebraic…
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
We introduce an innovative wavelet-based approach to dynamically adjust the local grid resolution to maintain a uniform specified error tolerance. Extending the work of Dubos and Kevlahan (2013), a wavelet multi-scale approximation is used…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and…