The aim of this study is to investigate the effect of boundary conditions on the accuracy and stability of the numerical solution of fluid flows in the context of single relaxation time Lattice Boltzmann method (SRT-LBM). The fluid flows are simulated using regularized, no-slip, Zou-He and bounce back boundary conditions for straight surfaces in a lid driven cavity and the two-dimensional flow ...

Numerous lattice Boltzmann (LB) methods have been proposed for solution of the convection–diffusion equations (CDE). For the 2D problem, D2Q9, D2Q5 or D2Q4 velocity models are usually used. When LB convection–diffusion models are used to solve a CDE coupled with Navier–Stokes equations, boundary conditions are found to be critically important for accurately solving the coupled simulations. Foll...

In this article, we numerically study the regularity loss of the solutions of non-parametric minimal surfaces with non-zero boundary conditions. Parts of the boundaries have non-positive mean curvature. As expected from theoretical results in such geometry, we find that the solutions may or may not satisfy the boundary conditions depending upon the data. Firstly, we validate the numerical study...

*Correspondence: [email protected] School of Applied Mathematics, Xiamen University of Technology, Xiamen, China Abstract The anisotropic parabolic equations with variable exponents are considered. If some of diffusion coefficients {bi(x)} are degenerate on the boundary, the others are always positive, then how to impose a suitable boundary value condition is researched. The existence of weak...

The trace identity of a differential operator deeply reveals the spectral structure of the differential operator and has important applications in the numerical calculation of eigenvalues. Here we refer to the references [2 – 11], with which the author became acquainted while doing research on the present paper. In [12], we obtained regularized trace formula for (1) with the boundary condition

In this paper we apply a regularized sinc method to compute the eigenvalues of a discontinuous Dirac systems, which contain eigenvalue parameter in one boundary condition, with transmission conditions at the point of discontinuity. The regularized technique allows us to insert some parameters to the well known sinc method; strengthening the existing technique and to avoid the aliasing error. Th...

In order to solve backward parabolic problems F. John [Comm. Pure. Appl. Math. (1960)] introduced the two constraints “‖u(T )‖ ≤ M” and ‖u(0) − g‖ ≤ δ where u(t) satisfies the backward heat equation for t ∈ (0, T ) with the initial data u(0). The slow-evolution-from-the-continuation-boundary (SECB) constraint has been introduced by A. Carasso in [SIAM J. Numer. Anal. (1994)] to attain continuou...

In order to solve backward parabolic problems F. John [Comm. Pure. Appl. Math. (1960)] introduced the two constraints “‖u(T )‖ ≤ M” and ‖u(0) − g‖ ≤ δ where u(t) satisfies the backward heat equation for t ∈ (0, T ) with the initial data u(0). The slow-evolution-from-the-continuation-boundary (SECB) constraint has been introduced by A. Carasso in [SIAM J. Numer. Anal. (1994)] to attain continuou...

The image system for the method of regularized Stokeslets is developed and implemented. The method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force. In order to satisfy zero-flow boundary conditions at a plane wall, the method of images derived for a standard (singular) Stokeslet is extended to give exact cancell...