Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation tha...

The band gap for 2D PhC with different modes and different lattice structures using FDTD have been computed. Three PBGs between the first and the second bands, between the second and the third bands and between the fourth and fifth bands are concluded. Simulation results shows that for band structure computation is of 1D PhC using FDTD, it is found that some additional solutions appear, which a...

This paper compares the continuous and discrete adjoint-based automatic aerodynamic optimization. The objective is to study the trade-off between the complexity of the discretization of the adjoint equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this p...

We develop a stable and high-order accurate finite difference method for problems in earthquake rupture dynamics in complex geometries with multiple faults. The bulk material is an isotropic elastic solid cut by pre-existing fault interfaces that accommodate relative motion of the material on the two sides. The fields across the interfaces are related through friction laws which depend on the s...

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation functi...

We propose a finite-difference algorithm for solving the time-dependent GinzburgLandau (TDGL) equation coupled to the appropriate Maxwell equation. The time derivatives are discretized using a second order semi-implicit scheme which, for intermediate values of the Ginzburg-Landau parameter κ, allows time-steps two orders of magnitude larger than commonly used in explicit schemes. We demonstrate...

A numerical analysis used to simulate the effects of wavy surfaces and thermal radiation on natural convection heat transfer boundary layer flow over an inclined wavy plate has been investigated. A simple coordinate transformation is employed to transform the complex wavy surface into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference...

In this work, some strategies and methods, based on finite-difference schemes, are introduced to model the propagation of acoustic waves in a three-dimensional fluid-solid configuration. Specifically, we have considered a heterogeneous propagation medium placed inside a 3D rectangular volume. A plane interface separates the volume into two regions: the first region is a fluid and the second one...

The variational inequality formulation provides a mechanism to determine both the option value and the early exercise curve implicitly [17]. Standard finite difference approximation typically leads to linear complementarity problems with tridiagonal coefficient matrices. The second order upwind finite difference formulation gives rise to finite dimensional linear complementarity problems with n...

We present finite difference schemes for solving the variable coefficient Poisson and heat equations on irregular domains with Dirichlet boundary conditions. The computational domain is discretized with non-graded Cartesian grids, i.e., grids for which the difference in size between two adjacent cells is not constrained. Refinement criteria is based on proximity to the irregular interface such ...