Math. Models Methods Appl. Sci. Downloaded from www.worldscientific.com by UNIVERSITY OF PITTSBURGH on 08/15/15. For personal use only. 2 K. Takizawa et al.representation of the circular paths associated with the spinning. The ST-SI method includes versions for cases where the SI is between fluid and solid domains with weaklyimposed Dirichlet conditions for the fluid and for cases where the SI is between a thin porous structure and the fluid on its two sides. Test computations with 2D and 3D models of a vertical-axis wind turbine show the effectiveness of the ST-SI method. -axis wind turbine.
ST-VMS method for flow computations with slip interfaces 3performances of the reconnect and renode options were evaluated. The evaluations showed that the force oscillations seen immediately after the remeshing are reduced substantially with the reconnect option.The ST variational multiscale (ST-VMS) method, 52,53 which was introduced recently, is the VMS version of the DSD/SST method. The VMS components are from the residual-based VMS method given in Refs. 59-62. The ALE-VMS method, 11,15,63 which preceded ST-VMS, is a moving-mesh extension of the VMS formulation originally proposed in Ref. 61. The ST methods, naturally, have higher accuracy for a given time-step size than the semi-discrete methods such as the ALE method (see Refs. 52 and 53 for the relevant accuracy analysis). Furthermore, the ST methods can be used with higher-order basis functions in time (such as NURBS 3,5,64,65 ). This gives us not only higher accuracy in solving the governing equations but also more effective ways of motion representation 24,52,53,66 and mesh moving and remeshing (see Refs. 24,[66][67][68][69][70]. We will explain that a few paragraphs later.Moving the fluid mechanics mesh to follow a fluid-solid interface enables us to control the mesh resolution near the interface, have high-resolution representation of the boundary layers, and obtain accurate solutions in such critical flow regions. These desirable features do not come easily or do not come at all with the nonmoving-mesh methods. As the mesh is not following the interface, independent of how well the interface geometry is represented, the resolution of the boundary layer will be limited by the resolution of the fluid mechanics mesh where the interface is.In computation of flow problems where one or more of the subdomains contain spinning structures, such as the rotor of a wind turbine, we want the mesh covering the subdomain containing the spinning structure to spin with it so that we maintain the high-resolution representation of the boundary layers. For that, something needs to be done at the interfaces between the subdomains. The ST computation of this class of problems was first accomplished with the shear-slip mesh update method (SSMUM), 71,72 which was introduced in Ref. 71 and named "SSMUM" in Ref. 72.The SSMUM was originally intended for flow around two high-speed trains passing each other in a tunnel. 71 The challenge was to accurately and efficiently update the meshes use...