Accelerated method of the Euler equations solution in transonic airfoil flow problem

The mathematical model based on the Clebsh variables, that approximates the Euler equations describing the ideal gas flows is proposed.The effective method of the calculation of such flows using the considered model is developed. This method is 10–20 times faster for the calculation of the airfoil flows compared to the direct Euler equations solution and its speed is practically the same as the speed of the velocity potential methods. The method needs the small modifications of the existent numerical methods of the potential equation solution. Comparison with the direct Euler equations solution shows satisfactory agreement for distributed and total aerodynamical characteristics up to the formation of strong shock waves, the case when the potential model gives essentially wrong results.