Simulation method utilizing cartesian grid

A simulation method utilizing a Cartesian grid comprising:

• a grid defining process in which a model of a two-dimensional or three-dimensional space is defined as a Cartesian grid composed of cells, the Cartesian grid being non-uniform;
• the Poisson equation defining process in which, based on a physical value and condition associated with the Cartesian grid, the Poisson equation
• ∇[k∇φ]=src expression (1)
• k:
• a constant defined for each cell individually,
• φ:
• a variable to be calculated and src:
• a source term
• is defined, and the Poisson equation being non-uniform such that the constants k defined for the cells of the Cartesian grid are not a fixed value;
• a calculating process performed by a computer in which, said physical value is calculated by approximately solving the Poisson equation,
• wherein the calculating process comprises:
• an error calculating step of calculating an error by using a Block-Cyclic Reduction Algorithm,
• a testing step of checking whether the calculated error is within a predetermined acceptable range or not, and
• an error correcting step of correcting the variable φ by the use of a correction parameter if the calculated error is outside the predetermined acceptable range, and
• said calculating process repeats said error calculating step, testing step and error correcting step until the error becomes within the predetermined acceptable range, whereby the Poisson equation is solved approximately,
• wherein in the error calculating step, an error (r) is defined as
• error(r)=src−A·φ
• src is the above-mentioned source term, φ is the above-mentioned variable,
• A is the matrix of the Poisson equation is calculated, and
• wherein zero is given to the φ in the first time computation of the error(r), and in the second time computation and the rest, the φ is given by
• φ=φold+φ′corr
• φold is the previous calculated value of the φ, φ′corr is the above-mentioned correction parameter indicating a correcting quantity to reduce the above-mentioned error and defined as
• φ′corr=Auni−1·[r/k_bar]
• k_bar is the average value of the values of k across all of the cells, and
• Auni−1 is the inverse matrix of a matrix of a uniform Cartesian grid having the same boundary conditions as those of said non-uniform Cartesian grid.