Related papers: Enhanced single-node boundary condition for the La…
A new volumetric-type boundary treatment is introduced for the lattice Boltzmann method. Populations are projected onto a discontinuous piecewise linear basis and streamed using an exact geometrical mapping. The method is implemented in 2D…
This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM…
We consider a waveguide modeled by the Laplacian in a straight planar strip. The Dirichlet boundary condition is taken on the upper boundary, while on the lower boundary we impose periodically alternating Dirichlet and Neumann condition…
In this work we investigate the issue of non-physical slip at wall of lattice Boltzmann simulations with the bounce-back boundary scheme. By comparing the analytical solution of two lattice models with four and nine discrete velocities for…
Using Sklyanin's classical theory of integrable boundary conditions, we use the Hamiltonian approach to derive new integrable boundary conditions for the Ablowitz-Ladik model on the finite and half infinite lattice. In the case of half…
A constraint penalization method is introduced within the Lattice Boltzmann (LBM) framework to model fluid-structure interactions involving rigid bodies. The proposed approach extends the fictitious domain concept by enforcing the…
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. By mapping lattice Boltzmann schemes to Finite Difference schemes, we…
We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order…
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
We review the first and second boundary value problems for the Stokes system posed in a bounded Lipschitz domain in $\mathbb{R}^n.$ Particular attention is given to the mixed boundary condition: a Dirichlet condition is imposed for the…
We present Helmholtz or Helmholtz like equations for the approximation of the time-harmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models…
In this paper, we propose a computational framework,which is based on a domain decomposition technique, to employ both finite element method (which is a popular continuum modeling approach) and lattice Boltzmann method (which is a popular…
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…
A transport equation with a non-smooth velocity field is considered under inhomogeneous Dirichlet boundary conditions. The spatial gradient of the velocity field is assumed in $L^{p'}$ in space and the divergence of the velocity field is…
We consider boundary element methods where the Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented…
The enhanced continualization approach proposed in this paper is aimed to overcome some drawbacks observed in the homogenization of beam lattices. To this end an enhanced homogenization technique is proposed and formulated to obtain…
We initiate the study of noncharacteristic boundary layers in hyperbolic-parabolic problems with Neumann boundary conditions. More generally, we study boundary layers with mixed Dirichlet--Neumann boundary conditions where the number of…
We deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, condition is prescribed on the…
We introduce a new boundary condition which renders the flux-insertion argument for the Lieb-Schultz-Mattis type theorems in two or higher dimensions free from the specific choice of system sizes. It also enables a formulation of the…