Method for calculating nonlinear partial differential equation by dual-grid iteration

Abstract

The invention discloses a method for calculating a nonlinear partial differential equation by dual-grid iteration. The method comprises the following steps: (a) establishing a three-dimensional geometric model of the nonlinear partial differential equation; (b) performing grid dissection on the three-dimensional geometric model, and dividing into two sets of grids, namely grids A and girds B, wherein the grids A are non-fitted grids, and the grids B are polyhedral fitting grids; (c) interpolating initial and boundary data into non-fitting parts of the grids A by using interpolations with four orders or above; (d) decomposing the nonlinear partial differential equation into a plurality of linear equations by using an iterative technique, wherein the linear equation is solved by using the grids A and using a four-order algorithm, and interpolating into the grids B to obtain fields in the fitting grids B; (e) performing iterative computation in the grids B; (f) repeating the steps (d) and (e) until the solving is ended. Compared with the prior art, the method disclosed by the invention has the advantages of high calculation efficiency, low cost and high precision by adopting dual-grid solving.

Description

technical field [0001] The invention relates to a method for double-grid iterative calculation of nonlinear partial differential equations. Background technique [0002] The numerical solution of nonlinear partial differential equations is a basic work in physics and mathematics. In the prior art, the partial differential equations are generally calculated by meshing, which has the following disadvantages: 1. Only through the geometric mesh Modification of grid subdivision (such as encryption, body-fitted subdivision, etc.) to overcome the problem of poor mesh quality caused by complex geometry. A poor quality grid will greatly reduce the calculation efficiency, and a poor grid will be several times the calculation time and cost of a good grid. 2. Complex geometry, due to the difficulty of geometry itself, when solving nonlinear problems, the accuracy will be greatly lost. What brings is that in order to obtain the required accuracy, more computing time and machine time are...

AI Technical Summary

Problems solved by technology

[0002] The numerical solution of nonlinear partial differential equations is a basic work in physics and mathematics. In the prior art, the partial differential equations are generally calculated by meshing, which has the following disadvantages: 1. Only through the geometric mesh Modification of grid subdivision (such as encryption, body-fitting subdivision, etc.) to overcome the problem of poor mesh quality caused by complex geometry

A poor-quality grid will greatly reduce the efficiency of calculations, and a poor grid will be several times the calculation time and cost of a good grid

2. Complex geometry, due to the difficulty of geometry itself, when solving nonlinear problems, the accuracy will be greatly lost. What brings is that in order to obtain the required accuracy, more computing time and machine time are required, cost and efficiency multiply

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