Application of the implicit method of characteristics on a regular grid for solving the gas-dynamic problems

In this work, an implicit method is proposed to numerically solve a system of the onedimensional nonstationary equations of gas dynamics transformed by the method of characteristics. Internal points of the channel for a solid-propellant charge are considered at a preignition period of the solid-propellant rocket engine operation. The use of the implicit method makes it possible to calculate the values of gas-dynamic parameters at nodal points of the regular coordinate grid. Calculations of the gas-dynamic parameters both when integrating over time and along the spatial coordinate are performed with the second order of accuracy. Both subsonic and supersonic flows are studied. It is shown that, when predicting the expected pressure value during the transition from one time layer to another with the second order of accuracy, the twenty-fold efficiency of the implicit method is achieved in comparison with the explicit difference method. The trial calculation is performed.