The Study Of Numerical Calculation For The New Model Of A Low-permeability Gas

The paper hopes to extract a solution of a nonlinear partial differential equation, a quite new model, of low-permeability gas reserves, then studies the penetraial character. The pose of the model has already been proved theoretically[4], which encourages us to seek an aptitude numerical calculation and to realize the computation.Considering the true background, when the model is discretized the flow rate and the volume must keep conservation[10]. There is a linear relation of the logarithm between The pressure difference in round seepage flow region and the radius, for the same accuracy,it is better to select a center mesh grid that is a isometry system with Inr interval.The calculation of The boundary of the coefficient of conductivity should be different from that of the volume of the net grid .When the model is discretized we get a nonlinear equations set.According to the set, extracting a solution of the model changes into doing so for the set at a different time step.The paper uses a homotopy with the parameter to research the solution of the set.The adaptive homotopy method uses the homotopy with parameter to get aenough good approximation XN of the genuine solution x , and then use theNewton iteration to attain a more precise one. While getting at somewhat precise result, the homotopy stop and the Newton iteration begins. When the precision of the solution answers for some criterion the process ceases and output the result.In the course of the homotopy or the Newton, the parameter will be changed when the singular case comes forth. After defining a new homotopy, the process begins with the new " Homotopy-->Newton" .If the times of renewing homotopy get at the max M , the net and nods get adjusting (at the same time, the set will be renewed in the paper), and the homotopy takes count from zero, and the process begins also with the new " Homotopy-->Newton "When the nodes attain to the max V , and the homotopy times attain to M too, it mean that the current process fails and process terminates abnormally.The paper has proved the convergence of the compound of the adaptive homotopy iteration of varying step length and the Newton iteraction, and improved the result of [ 18]the algorithm has a powerful adaptive capacity with " homotopy " and " net grid" - two-adjusting-method.The algorithm is realized through the programming.The enumrical value has a good approximation comparing with the true value. Analyzing these data ,the numerical value with the slippage effect or not, the true value, the model with the effect is better than without the effect. All mean:the model, the algorithm, and the programming success.