Finite Difference Scheme for Solving Parabolic Partial Differential Equations with Random Variable Input under Mean Square Sense

This study deal with seven points finite difference method to find the approximation solutions in the area of mean square calculus solutions for linear random parabolic partial differential equations. Several numerical examples are presented to show the ability and efficiency of this method.

Hall Effect on ECF Flow along a Rotating Infinite Porous Plate in the Presence of Transverse Magnetic Field

Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter 5 ≤ Pm ≤ 15 has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step τ = 1, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along x and z direction, couple stress along z direction, current densities along x and z direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.

Comparison of Mode Quality Factors for Equilateral Triangular, Square and Rhombus Optical Micro-Resonators

The mode frequencies and the quality factors for the equilateral triangular resonator (ETR), the square resonator (SR) and the rhombus resonator (RR) are numerically calculated by the finite difference time domain technique and the Padé approximation. The numerical results show that the resonant modes confined in an equilateral triangular cavity have much higher quality factors than those in the square or the rhombus cavities. The modes in the ETR are totally confined in transverse direction while those in the SR and RR are only partly confined. For the ETR with the side length of 4μm and the refractive index of 3 2, the mode quality factor of about 5 5×10 3 at the wavelength of 1 55μm has been obtained.

A Three-Dimensional Prediction Method for Thermal Diffusion

A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.