Study on Differential Equations Under Derivative of Arbitrary Mesh Node in Numerical Calculation of Flow and Heat Transfer
In numerical calculation of flow and heat transfer,derivative discretization is generally obtained by using Taylor formula and undetermined coefficient method to solve algebraic equations.For complex grid frame,the derivation process is complicated.In order to solve this problem,by observing the expressions of the first and second derivative and the cut of the nodes under the grid frame,this paper first guesses the general formula,and then proves the general formula of the derivative and the cut of the nodes.The expressions of the first derivative and the cut on the lower interface of any grid frame are obtained by taking the derivative of Lagrange interpolation.Compared with the traditional method,the differential general formula of derivative has the following advantages:1)It avoids the manual solution of equations and saves calculation time;2)It is easy to obtain high-precision difference expressions;3)Easy to compile general program,no need to re-discretize the equation after the change of the base point.The general differential formula of derivative and intercept derived in this paper has certain significance for obtaining the differential expression of derivative quickly and accurately
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