Numerical Solutions of Chaotic Convection Model in a Horizontal Layer of Fluid Using Deep Learning DNN

Abstract

In the subject of engineering, chaotic convection serves a critical function, for instance, magneto-mechanical devices, lasers, and mechanical and designing electrical circuits, as well as understanding fluid dynamics and oscillatory chemical reactions. Nonlinear chaotic systems, for instance, turbulence and fluid convection, exist up to modest external forcing levels before becoming unstable due to their extreme sensitivity to initial conditions. An uncontrolled system of convection will route the systems to unstable. When systems are unstable, it will damage the final product produced by industry such as microchips, crystal growth, welding of pipes line, etc. This paper developed a mathematical model for chaos convection in a fluid's horizontal layer derived using Galerkin truncated approximation techniques. Then, the obtained model was solved numerically using a multistep-deep learning neural network (DNN). We compared the results obtained graphically using multistep-DNN with the existing methods such as the Runge-Kutta method (RK), Euler method, and Livermore Solver for Ordinary Differential Equations (LSODE) method. It is found that multistep-DNN is able to solve the model efficiently and recover the results obtained using the RK method and LSODE method. However, for the Euler method, the results only cover small values of the Rayleigh number.