上游充通大学 2.1.2Euer方法 Shanghai Jiao Tong University 场论基本知识： x=(x,y,2)=(x1,x2,x3)=x(i=1,2,3) V=(u,y,w)=(w,u,w)=u,(i=1,2,3) 0 V= (aaa a Ox'oy'd x0x2x x (i=1,2,3) e.g., 7●V= Oxdy'dz ●(u,,w)= V= ax'ay'oz K 是Hamilton算子 Ow Ov ou 8y ay pressure p(x,t)-scalar(Oth order tensor) Te velocity (x,t)-vector (1st order tensor) T= =(6,j=1,2,3) stress (x,t)-2nd order tensorShanghai Jiao Tong University 2.1.2 Euler方法 场论基本知识： x y z O V ( ) ( ) ( ) 123 123 123 ( , , ) ( , , ) 1,2,3 ( , , ) ( , , ) 1,2,3 , , , , 1,2,3 e.g., , , (,, ) i i i i i xyz x x x x i uvw u u u u i i xyz x x x x uvw u uvw x yz x y z x = = == = = == ⎛ ⎞ ∂∂∂ ∂ ∂ ∂ ∂ ⎛ ⎞ = = == ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ∂∂∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎛ ⎞ ∂∂∂ ∂ ∂ ∂ ∂ • •= ⎜ ⎟ + + = ⎝ ⎠ ∂∂∂ ∂ ∂ ∂ ∂ x V V = ∇ ∇ pressure ( , ) - scalar (0th order tensor) velocity ( , ) - vector (1st order tensor) p t t x V x stress ( , ) - 2nd order tensor τ x t 是Hamilton算子 , , x y z ⎛ ⎞ ∂ ∂ ∂ ∇ = ⎜ ⎟ ⎝ ⎠ ∂ ∂ ∂ i jk wv uw vu i jk x yz yz z x xy uvw ∂∂∂ ∂ ∂ ∂∂ ∂∂ ⎛ ⎞ ⎛⎞ ⎛ ⎞ × = ⎜ ⎟ ⎜⎟ − + ⎜ ⎟ − + − ∂∂∂ ∂∂ ∂∂ ∂∂ ⎝ ⎠ ⎝⎠ ⎝ ⎠ r r r r r r 14243 1 14243 4243 ∇ V = , 1, 2, 3 ( ) xx xy xz yx yy yz ij zx zy zz i j τττ τττ τ τττ ⎡ ⎤ ⎢ ⎥ = == ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ τ