Inverse analysis of Navier–Stokes equations using simplex search method

The 2-D Navier–Stokes (N–S) equation is solved for the simultaneous estimation of three parameters such as the Reynold's number (Re), the length of the enclosure (lx) and the width of the enclosure (ly). The simplex search method (SSM) based on Nelder–Mead algorithm is used for minimizing the square of the error between a guessed centreline velocity field and an available one. For known values of the parameters such as Re, lx and ly, the reference field is first obtained by solving a forward problem using the finite difference method (FDM). To test the estimation accuracy corresponding to the reference field, next, an inverse problem is solved in which the above three parameters are taken as unknown variables. The estimation accuracy and the objective function are studied for the effects of initial guess, random and biased errors and CPU time. An excellent estimation of the unknowns is obtained using the SSM–FDM combination. The investigated errors have not found to contribute significantly to the estimation accuracy. Streamline patterns confirm that the centreline velocity field is sufficient to estimate the unknowns with an excellent accuracy.

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