TURBULENT KINETIC ENERGY IN AN APPROXIMATE SOLVER OF THE RIEMANN GAS DYNAMICS PROBLEM

The paper describes the consideration of turbulent kinetic energy in solving the gas-dynamic problem of discontinuity decay (Riemann problem) using the HLLC approximate solver. The system of Euler equations is considered with the addition of the hyperbolic equation of turbulent kinetic energy and consideration of turbulent pressure in the momentum and energy balance equations. The Jacobian coefficient of the system of equations and its eigenvalues are found. Based on this, changes are made to the calculation scheme in the HLLC solver. Using the Sod problem as an example, the correctness of taking into account turbulent kinetic energy in solving the Riemann problem is verified, and the instability of the scheme at high turbulent pressure is shown in the case of not taking turbulence into account in calculating the characteristic velocities.