Investigation of the numerical accuracy of shallow water flow estimation based on the ensemble Kalman filter using the SUPG FEM

ABSTRACT

The shallow water equation is employed as the governing equation to simulate flow behaviour in shallow water flow regions. The SUPG and the backward Euler methods, respectively, were employed for discretisation in space and time. In this paper, we carry out investigations on the numerical accuracy of shallow water flow estimation based on the ensemble Kalman filter using the SUPG FEM, and show the results of numerical experiments. The open channel model was employed as the numerical example in this study. The extended Kalman filter is generally employed to solve parameter identification problems. However, linearisation of the governing equation is carried out to apply parameter identification: it is known to be difficult to carry out computation reliably if problems that include a high degree of non-linearity need to be solved. On the other hand, linearisation of the governing equation is not carried out in the ensemble Kalman filter, so there is potential for the unknown parameter to be simultaneously identified in the computation of the data assimilation. The distribution of the unknown kinematic viscosity coefficient was therefore also investigated.