发表机构
Ege University（伊兹密尔经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文介绍二维不可压缩流求解器Motif，基于有限体积法、投影方法及多种数值方案，验证其精度与守恒性，为教学和直接数值模拟研究提供框架。
AI 中文摘要
本文档介绍了Motif的理论、实现和验证，Motif是一个二维不可压缩流求解器，作为教学和研究框架开发。控制方程在交错笛卡尔网格上使用有限体积法进行离散。对流项使用二阶Adams-Bashforth方法显式处理，扩散项使用Crank-Nicolson方法隐式处理，压力-速度耦合使用投影方法。考虑了标准投影和Perot（1993）的近似二阶投影。特别关注离散算子、边界条件、压力的时间处理、守恒性质以及数值耗散和色散。通过一系列周期、壁面约束和入口-出口流动问题，在均匀和光滑拉伸网格上验证了实现。检查了空间和时间收敛性、离散质量守恒、动能行为、涡度和能量谱。结果展示了空间离散的预期精度，并区分了两种投影方法的时间行为。本文档旨在足够详细地描述Motif以便独立实现，并检查与其持续发展至直接数值模拟相关的数值性质。
英文摘要
This document presents the theory, implementation, and verification of Motif, a two-dimensional incompressible flow solver developed as a teaching and research framework. The governing equations are discretized using the finite-volume method on staggered Cartesian grids. Convection is treated explicitly using the second-order Adams--Bashforth method, diffusion implicitly using the Crank--Nicolson method, and pressure--velocity coupling using projection methods. Both the Standard projection and the approximate second-order projection of Perot (1993) are considered. Particular attention is given to the discrete operators, boundary conditions, temporal treatment of pressure, conservation properties, and numerical dissipation and dispersion. The implementation is verified using a sequence of periodic, wall-bounded, and inlet--outlet flow problems on uniform and smoothly stretched grids. Spatial and temporal convergence, discrete mass conservation, kinetic-energy behavior, enstrophy, and energy spectra are examined. The results demonstrate the expected accuracy of the spatial discretization and distinguish the temporal behavior of the two projection approaches. The document is intended both to describe Motif in sufficient detail for independent implementation and to examine the numerical properties relevant to its continued development toward direct numerical simulation.
