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This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved formulation called the ``Smoothed Profile (SP) method'' is presented here in which…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
In this paper, we propose an approach for simulating wall-bounded incompressible turbulent flows by integrating the technology of random vortex method with the core principles of large-eddy simulations (LES). In particular, we employ the…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
A new and very general technique for simulating solid-fluid suspensions has been described in a previous paper (Part I); the most important feature of the new method is that the computational cost scales with the number of particles. In…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
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…
In this article, two novel numerical methods have been developed for simulating fluid/porous particle interactions in three-dimensional (3D) Stokes flow. The Brinkman-Debye-Bueche model is adopted for the fluid flow inside the porous…
Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap…
Simulations of over $10^3$ hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel…
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm…
This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…
In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…