We propose a θ-L approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies.The sharp-interface model is governed by surface d...We propose a θ-L approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies.The sharp-interface model is governed by surface diffusion and contact line migration.For solving the model,traditional numerical methods usually suffer from the severe stability constraint and/or the mesh distribution trouble.In the θ-L approach,we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables(i.e.,the tangential angle 6 and the total length L of the interface curve),so that it not only could reduce the stiffness resulted from the surface tension,but also could ensure the mesh equidistri-bution property during the evolution.Furthermore,it can achieve second-order accuracy when implemented by a semi-implicit linear finite element method.Numerical results are reported to demonstrate that the proposed θ-L approach is efficient and accurate.展开更多
基金This work was partially supported by the National Natural Science Foundation of China under Grant Nos.11871384(W.J.),12001034(W.H.),12001221(Y.W.),and 91630207(W.H.)the Fundamental Research Funds for the Central Universities under Grant CCNU19TD010(Y.W.)the Natural Science Foundation of Hubei Province under Grant Nos.2018CFB466(W.J.)and 2020CFB221(Y.W.).
文摘We propose a θ-L approach for solving a sharp-interface model about simulating solid-state dewetting of thin films with isotropic/weakly anisotropic surface energies.The sharp-interface model is governed by surface diffusion and contact line migration.For solving the model,traditional numerical methods usually suffer from the severe stability constraint and/or the mesh distribution trouble.In the θ-L approach,we introduce a useful tangential velocity along the evolving interface and utilize a new set of variables(i.e.,the tangential angle 6 and the total length L of the interface curve),so that it not only could reduce the stiffness resulted from the surface tension,but also could ensure the mesh equidistri-bution property during the evolution.Furthermore,it can achieve second-order accuracy when implemented by a semi-implicit linear finite element method.Numerical results are reported to demonstrate that the proposed θ-L approach is efficient and accurate.
基金E-Institutes of Shanghai Municipal Education Commission (E03004)Shanghai Municipal Education Commission (04DB07, 07ZZ64)+1 种基金Shanghai Science and Technology Committee (03QA14036)The Special Funds for Major Specialties of Shanghai Education Committee NSFC(1067130)
