Numerical Calculation of Convection with Reduced Speed of Sound Technique

TL;DR

This paper tests a method that artificially reduces the speed of sound in compressible fluid equations to enable larger time steps and improve parallel computing efficiency in stellar convection simulations, maintaining validity at low Mach numbers.

Contribution

The paper introduces and validates a hyperbolic, explicit numerical scheme that reduces the speed of sound to facilitate efficient simulations of stellar convection without frequent global communication.

Findings

Valid for effective Mach number less than 0.7

Enables larger time steps in simulations

Maintains accuracy of statistical quantities

Abstract

Context. The anelastic approximation is often adopted in numerical calculation with low Mach number, such as stellar internal convection. This approximation requires frequent global communication, because of an elliptic partial differential equation. Frequent global communication is negative factor for the parallel computing with a large number of CPUs. Aims. The main purpose of this paper is to test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. The reduction of speed of sound allows for larger time steps in spite of low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic and thus does not require frequent global communication. Methods. Two and three dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (due to reduction of speed of sound) are compared to test the validity of our approach. Results. Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the reduced speed of sound) remains less than 0.7.