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Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.

Supporting multi-language linking such as linking C and handwritten assembly modules in the verified compiler CompCert requires a more compositional verification technique than that used in CompCert just supporting separate compilation. The two extensions, CompCertX and Compositional CompCert, supporting multi-language linking take different approaches. The former simplifies the problem by imposing restrictions that the source modules should have no mutual dependence and be verified against certain well-behaved specifications. On the other hand, the latter develops a new verification technique that directly solves the problem but at the expense of significantly increasing the verification cost.In this paper, we develop a novel lightweight verification technique, called RUSC (Refinement Under Self-related Contexts), and demonstrate how RUSC can solve the problem without any restrictions but still with low verification overhead. For this, we develop CompCertM, a full extension of the latest version of CompCert supporting multi-language linking. Moreover, we demonstrate the power of RUSC as a program verification technique by modularly verifying interesting programs consisting of C and handwritten assembly against their mathematical specifications.

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Several automatic verification tools have been recently developed to verify subsets of LLVM’s optimizations. However, none of these tools has robust support to verify memory optimizations.In this paper, we present the first SMT encoding of LLVM’s memory model that 1) is sufficiently precise to validate all of LLVM’s intra-procedural memory optimizations, and 2) enables bounded translation validation of programs with up to hundreds of thousands of lines of code. We implemented our new encoding in Alive2, a bounded translation validation tool, and used it to uncover 21 new bugs in LLVM memory optimizations, 10 of which have been already fixed. We also found several inconsistencies in LLVM IR’s official specification document (LangRef) and fixed LLVM’s code and the document so they are in agreement.