Numerical Study on Propagation and Scattering of Sound by Two Cylinders

The propagation and scattering of sound by two rigid circular cylinders generated by a spatially distributed axisymmetric periodic acoustic source in the still air are simulated numerically using high-order compact spatial approximation of finite differences and high-order Runge-Kutta time integration. To solve the linearized Euler equations describing the wave propagation, the bipolar curvilinear coordinate system has been used in conservative and non-conservative variants. For bipolar curvilinear coordinate system, lines of the grid coincide with cylinders' envelopes for both cylinders. Use of bipolar coordinate system allows to solve the problem in frame of a single block finite difference methodology. The details of implementation of artificial boundary conditions are discussed for this transformation of coordinates. This study shows numerical robustness and long-time stability of high-order finite-difference compact computations in bipolar coordinates. The results on the fine 600x600 grid coincide well with the analytical solution. The main advantages of the proposed approach are a straightforward coordinate transformation of available single-block finite-difference code in Cartesian or polar coordinates and reasonable processor time.