tailieunhanh - The boundary element method with programming for engineers and scientists - phần 6

INTEGER, Ý ĐỊNH (IN):: Cdim! REAL chiều Cartesian, Ý ĐỊNH (IN):: r! Khoảng cách giữa nguồn và REAL điểm trường, Ý ĐỊNH (IN):: dxr (:) Khoảng cách trong Cartesian thư mục chia REAL R, Ý ĐỊNH (IN):: Vnorm (:)! Bình thường vector REAL:: dT (UBound (dxr, 1))! dT là mảng mờ giống như dxr REAL:: C | POSTPROCESSING 243 C 1 Pi r dU 1 C dxr 1 dU 2 C dxr 2 CASE 3 Three-dimensional solution C 1 Pi r 2 dU 1 C dxr 1 dU 2 C dxr 2 dU 3 C dxr 3 CASE DEFAULT END SELECT RETURN END FUNCTION dU FUNCTION dT r dxr Vnorm Cdim J------------------------------- derivatives of the Fundamental solution for Potential problems J Normal gradient J------------------------------- INTEGER INTENT IN Cdim J Cartesian dimension REAL INTENT IN r J Distance between source and field point REAL INTENT IN dxr JDistances in Cartesian dir divided by R REAL INTENT IN Vnorm J Normal vector REAL dT UBOUND dxr 1 J dT is array of same dim as dxr REAL C COSTH COSTH DOT_PRODUCT Vnorm dxr SELECT CASE Cdim CASE 2 J Two-dimensional solution C 1 Pi r 2 dT 1 C COSTH dxr 1 dT 2 C COSTH dxr 2 CASE 3 J Three-dimensional solution C 3 Pi r 3 dT 1 C COSTH dxr 1 dT 2 C COSTH dxr 2 dT 3 C COSTH dxr 3 CASE DEFAULT END SELECT RETURN END FUNCTION dT The discretised form of equation is u Pa EEA7ne Pa x-ĩl U Pa K e 1 n 1 e 1 n 1 where uen and tn are the solutions obtained for the temperature potential and boundary flow on node n on boundary element e and 244 The Boundary Element Method with Programming Te . Q N dSe Q u n ju Pa Q N dSe Q S S The discretised form of equation is given by En EN q Pa EE Se t -EEare J where qx S R xn q qy and AS . Asy ar . AR eyn q AS _ AR Rz. The components of AS and AR are defined as AS i U Pa Q NdS Q AS f U Pa Q N dS Q etc. ex y ey P. f Pa Q N dS Q R. f T Pa Q NndSQ etc. J ox Ị oy S S The integrals can be evaluated numerically over element e using Gauss Quadrature as explained in detail in Chapter 6. For 2-D problems this is AU ịư Pa Q Ek N Ek J EkWk k -I . _ AT e T Pa Q ík Nn ệk J k Wk k -1 and . au S n E u Pa Q k Nn Ek J Ek Wk etc. ox dT y T Pa Q Ek Nn Ek J EkWk etc. k i dy POSTPROCESSING 245 For 3-D problems the equations are M K Áun TJLu Pa Q k m Nn ệk m j ệk m wkWm m-1 k i M K à YYT Pa Q k m Nn ệk m J k m WkWm m 1 k