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Detailed data describing the motion of a rigid sphere settling in unperturbed fluid is generated by means of highly-accurate spectral/spectral-element simulations with the purpose of serving as a future benchmark case. A single…
In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time…
This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…
Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous…
In our recent work [H. Zhang, F.X. Trias, A. Oliva, D. Yang, Y. Tan, Y. Sheng. PIBM: Particulate immersed boundary method for fluid-particle interaction problems. Powder Technology. 272(2015), 1-13.], a particulate immersed boundary method…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
We present a black-box method to numerically investigate the linear stability of arbitrary multi-physics problems. While the user just has to enter the system's residual in weak formulation, i.e. by a finite element method, all required…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…
Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…
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…
We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…
We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…
We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…
In this work we numerically compute the bifurcation curve of stationary solutions for the free boundary problem for MEMS in one space dimension. It has a single turning point, as in the case of the small aspect ratio limit. We also find a…
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…
In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows.…