On the Numerical Approximation and Optimization Techniques for Solving an Inverse Cauchy Problem of Viscous-Burgers’ Equation
This paper deals with some inverse problems for nonlinear time-dependent PDEs in one spatial dimension, we investigate an inverse Cauchy problem that is settled by the nonlinear viscous Burgers equation. The viscous Burgers equation is a partial differential equation that is encountered in fluid dynamics studies, particularly in the domain of upward flow. The simplified model of the viscous Burgers equation explains the behavior of incompressible viscous fluid. The inverse Burgers problem belongs to a class of problems called ill-posed problems, which implies that there may be multiple sets of initial and/or boundary conditions that result in the same solution of the Burgers equation. To obtain robust and reliable solutions, it is essential to use regularization and cross-validation methods. However, it is often difficult to solve analytically, so numerical approaches are developed to overcome this difficulty. Domain decomposition (DDM) was used with alternative iterative methods. We performed a numerical reconstruction of the velocity and normal stress tensor that were vanished on an inaccessible part of the boundary using the over-prescribed noisy data obtained on the other accessible part of the boundary.
Volume & Issue
Vol. Volume 25 / Iss. Issue 4