二维瞬态非线性热传导问题的数值流形法求解OA

The numerical manifold method(NMM)effectively realizes the unified treatment of continuous and discontinuous problems through introduction of 2 cover systems:the mathematical cover for constructing the partition of unity functions and the physical cover for constructing the local approximation function.The appli-cation of the NMM to 2D transient nonlinear heat conduction problems was investigated.Firstly,based on the governing equations for the transient nonlinear heat conduction,along with the initial and boundary conditions,the weak form of the initial-boundary value problem was established.Subsequently,an NMM approximate ex-pression for the temperature field was presented and the global discretization form was derived with the Galer-kin method.For the time discretization,the backward Euler difference method was used and combined with the Newton-Raphson iterative method to solve the algebraic equations.From simulation of typical discontinuous plates with irregular boundaries and holes,the results show that,the NMM not only has high computational ac-curacy(the maximum error is not more than 0.6%)and good robustness,but also can handle complex geome-tries and discontinuous plates more effectively,which provides an innovative and efficient new method for nu-merical computation in this field.