New Godunov-type method for simulation of weakly compressible pipeline flows with allowance for elastic deformation of the walls

A new Godunov-type scheme for a complete nonlinear system of equations is developed as applied to the simulation of flows in an elastic deformable pipe. The proposed finite-difference method makes use of a one-dimensional grid, but the grid cells are characterized by two spatial sizes. The multidimensional effects and, primarily, pipe deformations are taken into account in the course of grid cell reconstruction. Difference relations are written for such a reconstructed grid. Due to the grid reconstruction procedure, the elastic deformation of the pipe can be taken into account directly without introducing the velocity of propagation of perturbations in the system “weakly compressible fluid-cylindrical shell.” The algorithm was shown to be highly accurate as applied to the water hammer problem.