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We present a simple modification of the direct-forcing immersed boundary method (IBM) proposed by Uhlmann [J. Comput. Phys, 2005] in order to enable it to be applied to particulate flows with solid-to-fluid density ratios around unity. The…
The lattice Boltzmann method (LBM) has shown its promising capability in simulating microscale gas flows. However, the suitable boundary condition is still one of the critical issues for the LBM to model microgaseous flows involving curved…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
In this study, we present a simulation-based numerical method for solving a class of singularly perturbed second-order differential equations that come from a simplified biologically motivated model of human gait. Important physical factors…
The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited…
We present a local detection method for dissipative particle dynamics (DPD) involving arbitrarily shaped geometric three-dimensional domains. By introducing an indicator variable of boundary volume fraction (BVF) for each fluid particle,…
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized…
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which…
A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
An extended immersed boundary method utilizing a semi-implicit direct forcing approach for the simulation of confined incompressible viscous thermal flow problems is presented. The method utilizes a Schur complement approach to enforce the…
A numerical method for simulation of bubble dynamics in three-dimensional potential flows is presented. The approach is based on the boundary element method for the Laplace equation accelerated via the fast multipole method implemented on a…
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…