A new inverse method based on Lattice Boltzmann method for 1D heat flux estimation

The general approach for methods of solving the Inverse Heat Conduction Problems (IHCP) is towards faster algorithms. One solution is to eliminate time-consuming iterations. The proposed method in this manuscript, as opposed to most traditional methods, is not based on trial-and-error algorithms. It uses a direct LBM solver to estimate the unknown heat flux. To do so, a new internal boundary condition is produced. Using this internal boundary condition and performing local computations of LBM will result in a direct estimation of the unknown heat flux. The results confirm a satisfactory accuracy. Also, the accuracy of the calculations is of first order, according to the number of time steps.