New time-marching methods for compressible Navier-Stokes equations with applications to aeroacoustics problems

Abstract

This paper derives a new class of time-marching methods of Runge-Kutta type (CERK) for the simulations of the two and three-dimensional compressible Navier-Stokes equations. Despite being implicit, the developed CERK methods do not require any numerical or analytical inversion of the coefficient matrix computationally explicitly. The efficiency and robustness of the developed methods are validated by solving the convection-diffusion equation and the unsteady compressible Navier-Stokes (NS) equations, which display stiff dynamical behavior at low Mach numbers. The performance of the developed methods is also compared with the representative explicit and implicit time-marching methods discussed in the literature. Several benchmark problems in computational aeroacoustics are analyzed by solving the NS equations using the developed time-marching methods. The computed results display an excellent match with the numerical and experimental results reported in the literature. For the computational aeroacoustics (CAA) problems, the computational costs required for the present methods are also compared with the methods noted in the literature.