The Direct And Inverse Problems Of The Influence On The Flow Fields Boundaries By The Moving Obstacle In An Ideal Fluid

Because of numerous potential applications,inverse problems in uid mechanicsconstitute a challenging topic. However,it is important to fishing,engineering, medicine,and even military,those are all meaningful and interesting areas. What is a littlequestion that the detection of a moving obstacle in uid. Because of an interest inthe detection of submarines underwater,I want to try to find the methods that movingobstacles in ideal uid is detected through the border ow field.That is to say I wantto know the relationship between the part of ideal uid border and moving obstacle ofit.Through reference ,the equations of the system solid and uid as follows:In these equations∈R2is a bounded rectangular area ,with the smooth boundary andΓm∈. let the ows is scalar function u in ,with the potential velocity ,g is theow through the boundary (just assumed to be given here),g satisfy : gdσ= 0,as long as the incoming ow ,located at the part of boundary where g < 0,as long as theoutow ,located at the part of boundary where g > 0, A rigid body occupying the setS(t)∈,the center of mess of it is h = (h1,h2),Settingl = h ,l∈R2. Thought theassumptions,the simplifies equations are:For the direct problem,we want get u by the given (h,l),change (7)-(9) to theboundary integral equations firstly:In the process of getting the boundary integral equations ,singular integral is appear-ance,to short-cut calculation, we pick up the collocation method to determine the pa-rameters,getting the system (2.19)-(2.23).We can obtain the discrete data uh(x).Throughthe numerical experiments,obviously,despite there is error by this numerical method,thereis still the correct property.The inverse problem has the same precondition with the direct,but the dierentgiven condition .Here we wang to get the data (h,l) that can describe the moving LetΓmis the distance from the node r to the node t in x0→x1,then computing the problemby same method to the direct.We gain the non-linear equations (3.5)-(3.10),the solutioncan be got by the Newton Method.In a word ,there are correct points in both direct and inverse problems,but stillneed for improving and further test in future.