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We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
Molecular dynamic (MD) simulation is used to study slip at the fluid-solid boundary in an unsteady flow based on the Stokes second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical…
We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that approximates no-slip boundary conditions with rapid linear…
We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
This work develops scientific computing techniques to further the exploration of using boundary control alone to optimize mixing in Stokes flows. The theoretical foundation including mathematical model and the optimality conditions for…
This paper sums up some recent validations of an immersed boundary method for compressible flow simulations. It has been already shown that this method is able to provide accurate results without meshing effort around more or less complex…
We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
In this paper, the boundary flex control problem of non stationary equation governing the coupled mass and heat flow of a viscous incompressible fluid in a generalized Boussinesq approximation by assuming that viscosity and heat…
Despite the advances in the field of generative models in computer vision, video stabilization still lacks a pure regressive deep-learning-based formulation. Deep video stabilization is generally formulated with the help of explicit motion…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
We study an optimal boundary control problem for the two-dimensional stationary micropolar fluids system with variable density. We control the system by considering boundary controls, for the velocity vector and angular velocity of rotation…
In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an…
We study boundary conditions applied to the macroscopic dynamics of Newtonian liquids from the view of microscopic particle systems. We assume the existence of microscopic boundary conditions that are uniquely determined from a microscopic…
This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance…
We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…