2002/03/31 by Masato Ida
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Heat Transfer #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.1016/s0010-4655(02)00691-4
published as Comput. Phys. Commun. 150 (3) pp.300-323 (2003) · 34 pages, 13 figures, elsart; Typo in Eq.25 corrected; Published
arxiv created 2002/12/25 · openalex publication_date 2002/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure) method, which is a pressure-based semi-implicit solver for the Euler equations of fluid flows. In Part I of this series of articles [M. Ida, Comput. Phys. Commun. 132 (2000) 44], we proposed an improved scheme for the convection terms in the equations, which allowed us discontinuous descriptions of the density interface by replacing the cubic interpolation function used in the CIP scheme with a quadratic extrapolation function only around the interface. In this paper, as Part II of this series, the multi-time-step integration technique is adapted to the CIP-CUP integration. Because the CIP-CUP treats different-nature components in the fluid equations separately, the adaptation of the technique is straightforward. This modification allows us flexible determinations of the time interval, which results in an efficient and accurate integration. Furthermore, some additional discussion on our methods is presented. Finally, the application results to composite flow problems such as compressible and incompressible Kelvin-Helmholtz instabilities and the dynamics of two acoustically coupled deformable bubbles in a viscous liquid are provided.