Abstract. Motivated by lubrication problems, we consider a micropolar fluid flow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < ε << 1. We prove the existence and uniqueness of a solution of this problem for any value of ε and we establish some a priori estimates. Then we use the two-scale convergence technique to derive the l...

In the last decades it has been recognized that the very high Rayleigh number convective boundary layer (CBL) has more complex nature than might be reckoned. Besides the fully organized component naturally considered as the mean flow and the chaotic small-scale turbulent fluctuations, one more type of motion has been discovered, namely, long-lived large-scale structures, which are neither turbu...

We introduce a combinatorial curvature flow for piecewise constant curvature metrics on compact triangulated 3-manifolds with boundary consisting of surfaces of negative Euler characteristic. The flow tends to find the complete hyperbolic metric with totally geodesic boundary on a manifold. Some of the basic properties of the combinatorial flow are established. The most important one is that th...

The spline finite strip method (S.F.S.M.) for buckling analysis of plates and plate assemblies subjected to longitudinal compression and bending, transverse compression as well as shear is described. The method allows for the boundary conditions. Local buckling coefficients of plates with different boundary conditions under compression, bending and shear are calculated. Convergence studies with...

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu&apos;s problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

The spline finite strip method (S.F.S.M.) for buckling analysis of plates and plate assemblies subjected to longitudinal compression and bending, transverse compression as well as shear is described. The method allows for the boundary conditions. Local buckling coefficients of plates with different boundary conditions under compression, bending and shear are calculated. Convergence studies with...

in this paper, free vibration of an Euler-Bernoulli beam with variable cross-section resting on elastic foundation and under axial tensile force is considered. Beam’s constant height and exponentially varying width yields variable cross-section. The problem is handled for three different boundary conditions: clamped-clamped, simply supported-simply supported and clamp-free beams. First, the equ...

The Interpolated Bounce-Back (IBB) method and Immersed-Boundary (IB) method are compared for fluid-solid boundary conditions in the Lattice Boltzmann Equation (LBE) in terms of their numerical accuracy and computational efficiency. We carry out simulations for the flow past a circular cylinder asymmetrically placed in the channel in two dimensions with the Reynolds number Re = 20 and 100, corre...

In this article, computational results from boundary integral equations and their normal derivatives for the same test cases are compared. Both kinds of formulations are desingularized on their real boundary. The test cases are chosen as a uniform flow past a circular cylinder for both the Dirichlet and Neumann problems. The results indicate that the desingularized method for the standard bound...