{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"95901\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"modified_tdt":"2015-11-02T00:00:00Z","thumb_s":"/61/44/61446e4abf57ec2f515f9da87d0e0a2da89e2722.jpg","oldid_t":"compsci 3719","setname_s":"ir_computersa","file_s":"/d6/2d/d62db855c6afee2cc2dc99c9adfdee6f2de95e18.pdf","title_t":"Page 69","ocr_t":"at the previous time st p, and h is the tim step size. This clos d ~ rm olu ti n i u d t compute the rotation angle of the normal vector about the streamline. h only unknown values involved in this solution are u(~~) and its velocity magnitud . On e a new point~~ of a streamline is computed, u(~~) can be calculated by using Equation 5.4. Th major computational costs of this solution include a vector field interpolation, a vector-vector addition and a vector inner product. 5.5.3 Solution for the Radius of Streamtube The governing equation of streamtube radius is shown in Equation 5.7. This ODE can be solved analytically: j rh 1 -dr ro r 1 fh 2 lo '\\ly. udt, 1 ih ln(ro) = - '\\ly. udt, 2 0 1 fh fh du' ln(ro) + 2(1o v. udt- lo de dt). From Equations 5.8, the divergence of u is a constant: and I I d~ = u dt. Therefore, (5.12) where rh is the streamtube radius at the current step, r 0 is the radius at the previous step, and u~ and u~ are the velocity magnitudes at the previous step and the current step. Since there is no unknown value in the right hand side of the equation, the cost of calculating rh is composed of only a few scalar multiplications and two function calls. From this equation, we can see that faster velocity results in a smaller radius. For incompressible flow, in which the divergence is zero, our result is equivalent to that obtained in [36].","restricted_i":0,"id":95901,"created_tdt":"2015-11-02T00:00:00Z","format_t":"application/pdf","parent_i":95941,"_version_":1642982571753078786}]},"highlighting":{"95901":{"ocr_t":[]}}}