Research For Solving Helmholtz Equation With Interface

IIM which based on IBM has been generally applied to solving complex fluidproblem It has second order precision,and applied uni％rm Cartesian grid,sothat mesh generation was very easy and fast In complex fluid problem with in—terface,coefficient,source term and flux function may become discontinued,i eexist jump Selecting proper local coordinate system and modifying the finitedifferent scheme by jump condition,IIM not only improve the order,but alsopreserve characteristic of finite different scheme,we can use the existed softwareto solve the problem quicklyIn this paper,we mainly applied IIM to solve Helmholtz—Poisson equationin three dimension,modified local coordinate system and interpolation scheme,so the procedure of IIM become effective and easy we use level set method torepresent the interface,classify all the grid points into regular points and irregularpoints At the regular points,we get the classic finite different scheme；At theirregular points．we get a finite different scheme with a correction term Thus．weobtain a global second order precision finite different scheme we also introducethe fast IIM,which use GMRES to solve the linear systems...