In this paper, implementation of an extended form of a no-slip wall boundary condition is presented for the three-dimensional (3-D) lattice Boltzmann method (LBM) for solving the incompressible fluid flows with complex geometries. The boundary condition is based on the off-lattice scheme with a polynomial interpolation which is used to reconstruct the curved or irregular wall boundary on the ne...

This paper deals with free vibration analysis of thick Laminated curved panels with finite length, based on the three-dimensional elasticity theory. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Fre...

We propose a method to generate high-order unstructured curved meshes using the classical Winslow equations. We start with an initial straight-sided mesh in a reference domain, and fix the position of the nodes on the boundary on the true curved geometry. In the interior of the domain, we solve the Winslow equations using a new continuous Galerkin finite element discretization. This formulation...

This paper treats a free boundary problem in two-dimensional excitable media arising from a singular limiting problem of a FitzHugh–Nagumo-type reaction-diffusion system. The existence and uniqueness up to translations of two-dimensional traveling curved waves solutions is shown. To study the stability of the waves, the local and global existence and uniqueness of solutions to the free boundary...

Curved boundary treatments provide a means of improving the computational accuracy of the conventional stairshaped approximation used in lattice Boltzmann (LB) simulations. Furthermore, curved boundary treatments can be extended to the modeling of moving boundary problems simply by adding a momentum term to the bounced distribution functions at the solid surface. This study commences by investi...

A (not necessarily convex) object C in the plane is -curved for some constant , < 1, if it has constant description complexity, and for each point p on the boundary of C, one can place a disk B whose boundary passes through p, its radius is diam(C) and it is contained in C. We prove that the combinatorial complexity of the boundary of the union of a set C of n -curved objects (e.g., fat ellipse...