płyta-bez-odsysania.docx

Równanie NS Płyta: dVdt+∂Vy∂t+Vx∂Vx∂x+Vy∂Vy∂y+Vz∂Vz∂z=Y-1ρ*∂P∂x+νΔVy+ν3*∂∂y(divV)|    , Vx=Vz=0y→0Vy=u→∂Vu∂y=0wektorV=iVx+jVy+kVz=iV+ju+kw ∆Vy=∆u=∂u∂t=∂2u∂x2+∂2u∂y2+∂2u∂z2→∂u∂t=v∂2u∂y→kierunek x |u=fy,t;∂p∂u=0→kierunek y| war. brzeg.:y=0;t≥0→u0,t=0 | S=yνt;∂u∂t=∂u∂s∂s∂t=∂u∂s1νx*-12t32=-12xt-12vt*∂u∂t=-12st∂u∂t |∂u∂y=∂u∂s∂s∂y=∂u∂s1νt→∂2u∂y2=∂∂y∂u∂s1νt=1νt∂∂y∂u∂s=1νt∂∂s∂u∂y=1νt ∂∂s(1νt ∂u∂s)= 1vt∂2u∂s2 -12stduds=v1vtd2uds2d2uds2+12sduds=0\:duds |ddsdudsduds=-12s\*| lnduds=-12sds=-14s2+C1| duds=e-14s2+C=Ce-s22 *0s| u(ss^s=XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX)-u(0)=C10se-s22 ds zmiana zzmiana XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXmiennych s=ξschnnXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX   s2=ξ→ds=2dξ ;s=2ξ| uξ-u(0)=C02ξe-ξ2 dξ   |0-uo=C0∞e-ξ2 dξ=cπ...