This article deals with the finite-element RKDG method (Runge-Kutta Discontinuous Galerkin) and its application for numerical integration of three-dimensional system of equations of ideal gas on unstructured grids. By means of the described algorithm we solved two test tasks. For each task we conducted the analysis and compared the task solution with well-known analytical solutions or with tabular data. We also give error assessment in the solution.
Dimitrienko Y., Koryakov M., Zakharov A. Application of RKDG method for computational solution of three-dimensional gas-dynamic equations with non-structured grids. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 75-91
In the article we propose an algorithm for the numerical simulation of conjugate gasdynamic and thermomechanical processes in composite structures of high-speed aircraft. The algorithm allows calculating all parameters of the three-dimensional gasdynamic flow near the surface of the aircraft, heat exchange on the surface, heat and mass transfer processes in the internal structure of thermodestructive polymer composite, as well as processes of composite construction thermodeformation, including the effects of changes in the elastic characteristics of the composite, variable thermal deformation, shrinkage caused by thermal degradation, building up interstitial gas pressure in the composite. An example of numerical simulation of conjugated processes in a model composite construction of high-speed aircraft illustrates the possibilities of the proposed algorithm.
Dimitrienko Y., Koryakov M., Zakharov A., Stroganov A. Computational modeling of conjugated gasdynamic and thermomechanical processes in composite structures of high speed aircraft. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 3-24