Application of grid-characteristic method for numerical solution of deformable solid mechanics dynamical problems
Abstract
The grid-characteristic method is a promising numerical method for solving hyperbolic systems of equations, e.g., equations describing elastic and acoustic waves. This method has high precision and allows you to physically correctly simulate wave processes in heterogeneous media. The grid-characteristic method makes it possible to correctly take into account boundary conditions and conditions on surfaces with different physical characteristics. Most fully the advantages of the method are for one-dimensional equations, especially in combination with a fixed difference grid, as in conventional grid-based methods. However, in the multidimensional case using the algorithms of splitting with respect to spatial variables, the author has managed to preserve its positive qualities. The use of the method of Runge – Kutta type, or integro-interpolation method for hyperbolic equations makes it possible to effectively carry out the generalization of methods developed for linear equations, in nonlinear case, in particular, to enforce the difference analogs of the conservation laws, which is important for shock-capturing, for example, discontinuous solutions. Based on the author's variant of the grid-characteristic method were numerically solved several important problems of seismic prospecting, seismic resistance, global seismic studies on Earth and Mars, medical applications, nondestructive testing of railway lines, the simulation of the creation and characteristics of composite materials for the aerospace industry and other areas of practical application. A significant advantage of the constructed method is the preservation of its stability and precision at the strains of the environment. This article presents the results of numerical solution based on the grid-characteristic method to the problem of modeling elastic-plastic deformation in traumatic brain injury.
Keywords
hyperbolic type equations,
elastic and plastic deformation,
grid-characteristic method,
finite difference schemes,
discontinuous solutions
Supporting agencies: The research is done within the frame of the independent R&D.
About the Author
Igor B. Petrov
Moscow Institute of Physics and Technology (State University), Moscow, Russian Federation
Russian Federation
Russian Federation
Petrov, Igor B., Correspondent Member of RAS, Dr.Sci. (Phys. -Math.), Professor, Moscow Institute of Physics and Technology (State University), Moscow, Russian Federation
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Review
For citations:
Petrov I.B. Application of grid-characteristic method for numerical solution of deformable solid mechanics dynamical problems. Computational Mathematics and Information Technologies. 2017;1(1).
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