The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechan...The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.展开更多
The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite di...The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite difference method. Moreover, this feature has made it one of the most-promising meshless methods because it also allows us to reduce the time-consuming task of mesh generation and the numerical solution of integrals. This characteristic allows us to shape geological features easily whilst maintaining accuracy in the results, which can be a source of great interest when dealing with this kind of problems. Two widespread geophysical investigation methods in civil engineering are the cross-hole method and the seismic refraction method. This paper shows the use of the GFDM to model the aforementioned geophysical investigation tests showing precision in the obtained results when comparing them with experimental data.展开更多
基金Supported by the National Natural Science Foundation of China (Nos.50876114 and 10602043)the Program for New Century Excellent Talents in University,and the Scientific Research Key Project Fund of Ministry of Education (No.106142)
文摘The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.
基金The authors acknowledge the support of the Escuela Tecnica Superior de Ingenieros Industriales(UNED)of Spain,project 2019-IFC02of the Universidad Politecnica de Madrid(UPM)(Research groups 2019).
文摘The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite difference method. Moreover, this feature has made it one of the most-promising meshless methods because it also allows us to reduce the time-consuming task of mesh generation and the numerical solution of integrals. This characteristic allows us to shape geological features easily whilst maintaining accuracy in the results, which can be a source of great interest when dealing with this kind of problems. Two widespread geophysical investigation methods in civil engineering are the cross-hole method and the seismic refraction method. This paper shows the use of the GFDM to model the aforementioned geophysical investigation tests showing precision in the obtained results when comparing them with experimental data.
