Modernized and Parallelized Mapped Legendre Spectral Method Code for Unbounded Vortical Flow Simulations

A modernized and parallelized flow simulation code package is presented, along with its scaling performance results, using several example rotating flow problems in an unbounded domain. The code package, MLegS—standing for Mapped Legendre Spectral expansion that accounts for the domain's unboundedness—employs associated Legendre functions with an algebraic mapping as the basis elements for the radial expansion of an arbitrary field quantity. Based on the numerical algorithm proposed by Matsushima & Marcus (J. Comput. Phys., vol. 137, no. 2, 1997, 321-345), MLegS incorporates scalable multiprocessing interfaces for high-performance computing, supported by the utilization of temporary multiple-precision arithmetic, which enables access to a larger number of basis elements with a higher normalization factor than is attainable with typical double-precision computing. Weak or strong scaling test results are provided for sample problems, and the potential extensive applications of the code package are discussed.