In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics finite element method for the discretization of the space variables, and we design a multirate iterative scheme on the time scale which solve a generalized Stokes problem in the coarse time size and solve the diffusion problem in the finer time size according to the characteristics of the poroelasticity problem. Secondly, we prove that the multirate iterative scheme is stable and the numerical solution satisfies some energy conservation laws, which are important to ensure the uniqueness of solution to the decoupled computing problem. Also, we analyze the error estimates to prove that the proposed numerical method doesn't reduce the precision of numerical solution and greatly reduces the computational cost. Finally, we give the numerical tests to verify the theoretical results and draw a conclusion to summary the main results in this paper.
翻译：在本文中,我们为液体饱和孔径弹性模型提出了一个多功能迭代方案。 首先,我们将原始模型重新组合成一个流体并存的问题,以应用多物理有限元素方法将空间变量分解,我们在时间尺度上设计一个多层迭代方案,解决粗糙时间大小的普遍斯托克斯问题,并根据孔径性问题的特点,解决更细时间尺寸的传播问题。 其次,我们证明多层迭代方案是稳定的,数字解决方案符合一些节能法,这对于确保解开的计算问题的解决办法的独特性非常重要。此外,我们分析误差估计数,以证明拟议的数字方法不会降低数字解决方案的精确性,大大降低计算成本。最后,我们用数字测试来核实理论结果,并得出总结本文的主要结果。
相关内容
微信扫码咨询专知VIP会员