UNCERTAINTY QUANTIFICATION FOR THERMOMAGNETIC CONVECTION OF PARAMAGNETIC FLUID IN RANDOM POROUS MEDIA BASED ON INTRUSIVE POLYNOMIAL CHAOS METHOD

At present, the research of fluid flow and heat transfer problems is mostly based on deterministic working conditions, but there are a large number of uncertain factors in real fluid flow and heat transfer problems. The uncertainty quantification of computational fluid dynamics provides an ability to understand the influence of uncertain factors such as fluid physical properties, boundary conditions and initial conditions on simulations results. In order to reveal the propagation law and evolution characteristics of thermomagnetic convection of paramagnetic fluid in random porous media, a mathematical model and algorithm program of uncertainty quantification for thermomagnetic convection were developed based on intrusive polynomial chaos expansion method. In this method, the input random parameters and output response were expressed by Karhunen-Loeve expansion and polynomial chaos expansion respectively. At the same time, the Galerkin projection method was adopted to decouple the stochastic control equations into a set of deterministic control equations which can be solved by finite element correction method, and each polynomial chaos of output response was solved. Finally, the stochastic projection method was used to solve the chaos coefficients in the corresponding deterministic control equations, and the statistical characteristics and chaos effect of the output response are obtained. The uncertainty quantification of thermomagnetic convection shows that the porosity uncertainty of porous media affects the thermomagnetic convection of paramagnetic fluid in a square cavity through the evolution of governing equations, and the thermomagnetic convection of paramagnetic fluid presents a significant chaos effect. The output response shows the characteristics of rapid convergence. The output response values in the first-order mode are at least one order of magnitude lower than the corresponding average values, while the output response values in the second-order mode are much smaller than those in the first-order mode. Compared with the Monte Carlo method, the two results agree well, but the computational cost of the intrusive polynomial chaos expansion method is significantly reduced.