The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These me...The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These methods allow to effectively suppress oscillations,including in velocity profiles,as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations.The methods can be applied both in explicit and implicit(method of separate sweeps)iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer,as well as in solving problems of magnetohydrodynamics and computational astrophysics.In order to avoid loss of solution accuracy on spatially non-uniform grids,in this work an algorithm of grid embeddings is developed,which is applied near transition points between cells of different sizes.The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes.Calculations are performed for the classical problem of decay of an arbitrary discontinuity(Sod’s problem)and the problem of propagation of two symmetric rarefaction waves in opposite directions(Einfeldt’s problem).In the case of using different methods for selecting the AAV,a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed.As a result of the comparative analysis,the applicability of these methods is shown in the spatially one-dimensional case(explicit and implicit iterative processes).The obtained results are compared with the data from the literature.The results coincide with analytical solutions with high accuracy,where the relative error does not exceed 0.1%,which demonstrates the effectiveness of the developed algorithms and methods.展开更多
基金carried out within the framework of the state assignment of KIAM RAS(No.125020701776-0).
文摘The work presents new methods for selecting adaptive artificial viscosity(AAV)in iterative algorithms of completely conservative difference schemes(CCDS)used to solve gas dynamics equations in Euler variables.These methods allow to effectively suppress oscillations,including in velocity profiles,as well as computational instabilities in modeling gas-dynamic processes described by hyperbolic equations.The methods can be applied both in explicit and implicit(method of separate sweeps)iterative processes in numerical modeling of gas dynamics in the presence of heat and mass transfer,as well as in solving problems of magnetohydrodynamics and computational astrophysics.In order to avoid loss of solution accuracy on spatially non-uniform grids,in this work an algorithm of grid embeddings is developed,which is applied near transition points between cells of different sizes.The developed algorithms of CCDS using the methods for AAV selection and the algorithm of grid embeddings are implemented for various iterative processes.Calculations are performed for the classical problem of decay of an arbitrary discontinuity(Sod’s problem)and the problem of propagation of two symmetric rarefaction waves in opposite directions(Einfeldt’s problem).In the case of using different methods for selecting the AAV,a comparison of the solutions of the Sod’s problem on uniform and non-uniform grids and a comparison of the solutions of the Einfeldt’s problem on a uniform grid are performed.As a result of the comparative analysis,the applicability of these methods is shown in the spatially one-dimensional case(explicit and implicit iterative processes).The obtained results are compared with the data from the literature.The results coincide with analytical solutions with high accuracy,where the relative error does not exceed 0.1%,which demonstrates the effectiveness of the developed algorithms and methods.
