Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source

The thermal problem of functionally graded materials (FGM) under linear heat source is studied by a hybrid numerical method. The accuracy of the analytical method and the efficiency of the finite element method are taken into account. The volume fraction of FGM in the thickness direction can be changed by changing the gradient parameters. Based on the weighted residual method, the heat conduction equation under the third boundary condition is established. The temperature distribution of FGM under the action of linear heat source is obtained by Fourier transform. The results show that the closer to the heat source it is, the greater the influence of the heat source is and the influence of the heat source is local. The temperature change trend of the observation points is consistent with the heat source, showing a linear change. The results also show that the higher the value of gradient parameter is, the higher the temperature of location point is. The temperature distribution of observation points is positively correlated with gradient parameter. When the gradient parameter value exceeds a certain value, it has a little effect on the temperature change in the model and the heat conduction in the model tends to be pure metal heat conduction, the optimal gradient parameters combined the thermal insulation property of ceramics and the high strength toughness of metals are obtained.

Numerical Investigation of Rising Vapour Bubble in Convective Boiling Using an Advanced 3D Hybrid Numerical Method

This chapter introduces an advanced and new type of Three-Dimensional (3D) numerical method called the InterSection Marker (ISM) method. The ISM method - a hybrid Lagrangian–Eulerian 3D front-tracking algorithm specifically crafted for multi-phase flow simulation. The method was used to simulate rising vapour bubble behaviour in Convective boiling conditions. Two applications: bubble growth and bubble condensation due to the convective action, were investigated. Numerically obtained bubble properties, such as size, shape and velocity, are compared well against the past works, and the ISM method proved to be an efficient numerical tool for the interface tracking of multi-phase flow CFD simulations involving heat and mass transfer.

An Order Four Continuous Numerical Method for Solving General Second Order Ordinary Differential Equations

Continuous hybrid methods are now recognized as efficient numerical methods for problems whose solutions have finite domains or cannot be solved analytically. In this work, the continuous hybrid numerical method for the solution of general second order initial value problems of ordinary differential equations is considered. The method of collocation of the differential system arising from the approximate solution to the problem is adopted using the power series as a basis function. The method is zero stable, consistent, convergent. It is suitable for both non-stiff and mildly-stiff problems and results were found to compete favorably with the existing methods in terms of accuracy.

Модифицированная теория связанных волн и численный метод для анализа брэгговских зеркал с произвольным профилем показателя преломления

An analytical and effective numerical approach to the analysis of the optical characteristics of Bragg mirrors with an arbitrary refractive index profile is developed. Analytical expressions obtained using the modified theory of coupled waves for the coefficients of reflection / transmission of light from / through the BM with high accuracy predict its main characteristics at both low and high contrast of the refractive index. The hybrid numerical method includes the numerical calculation of the transfer matrix for one period of the knowledge base and its analytical multiplication for an arbitrary number of periods. The developed methods are applied to the analysis of the properties of practically important BMs made on the basis of sprayed pairs of Ta2O5 / SiO2 dielectrics, Group III nitrides and arsenides. The characteristics of the knowledge base with smooth (gradient) interfaces are considered in detail.

An Explicit Hybrid Method for the Nonlocal Allen–Cahn Equation

We extend the explicit hybrid numerical method for solving the Allen–Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.