On initial, boundary conditions and viscosity coefficient control for Burgers' equation

• Published in: International journal for numerical methods in fluids 1998-07, Vol.28 (1), p.113-128
• Main Authors: Leredde, Y., Lellouche, J.-M., Devenon, J.-L., Dekeyser, I.
• Format: Article
• Language: English
• Subjects: adjoint model; Burgers' equation; Computational methods in fluid dynamics; data assimilation; Earth, ocean, space; Exact sciences and technology; External geophysics; Fluid dynamics; Fundamental areas of phenomenology (including applications); optimal control; Other topics; Physics; Physics of the oceans; Radioactivity
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19980715)28:1<113::AID-FLD702>3.0.CO;2-1

In order to use the optimal control techniques in models of geophysical flow circulation, an application to a 1D advection–diffusion equation, the so‐called Burgers' equation, is described. The aim of optimal control is to find the best parameters of the model which ensure the closest simulation to the observed values. In a more general case, the continuous problem and the corresponding discrete form are formulated. Three kinds of simulation are realized to validate the method. Optimal control processes by initial and boundary conditions require an implicit discretization scheme on the first time step and a decentered one for the non‐linear advection term on boundaries. The robustness of the method is tested with a noised dataset and random values of the initial controls. The optimization process of the viscosity coefficient as a time‐ and space‐dependent variable is more difficult. A numerical study of the model sensitivity is carried out. Finally, the numerical application of the simultaneous control by the initial conditions, the boundary conditions and the viscosity coefficient allows a possible influence between controls to be taken into account. These numerical experiments give methodological rules for applications to more complex situations. © 1998 John Wiley & Sons, Ltd.