Program code developpment experience based on Galerkin method with discontinuous basic functions of high order of accuracy

Аuthors

Podaruev V. Y.

Central Aerohydrodynamic Institute named after N.E. Zhukovsky (TsAGI), 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia

Abstract

The paper enunciates the experience of developing the software based on the Galerkin method with discontinuous basis functions of high accuracy. The purpose of the work consists in describing the specifics of of the program code developing intended for use on a multiprocessor computer system. The methodollogy of the work is based on the modern approach to simulation of complicated 3D flows using Galerkin scheme with discontinuous basis functions. The methodology of this work execution includes theoretical analysis of the method, application of modern approaches to programming, verification and validation of employed ideas and demonstration of the developed code’s suitability for complicated nonlinear calculations. The result of the work are recommendations for the software developing based on modern methods of computational aerodynamics.

To develop a software interface for specific codes, it is convenient to use the Python programming language. Before proceedeing to descring the computational domain topology, the calculated grid type (structured or unstructured) should be defined. It is necessary to determine what types of geometric objects are to be worked with. In the case of “serendipian” elements, the desired order of the problem approximation should be selected and the elements for linear, quadratic, cubic, etc. cases should be identified, with further changing only the sets of shape functions, characteristic to the specified elements. It is convenient herewith to realiize these sshape functions in the form of the so-called “lambda” functions included in the C++ standard.

The results of this work can be applied for educational purposes in technical universities and in practical works on developing new software in scientific institutes and design offices. The main conclusion of the paper is that a high-order scheme allows diminish entropic errors while calculating the flow after stagnant zones, as well as calculate all the flow specifics, which are characteristic for flow around the high-lift wing with released slats and flaps. Modern programming approaches allow ensure the high code scalability. In addition, the main features of the Galerkin method with discontinuous functions, such as reconstruction of conservative variables, the approximation of convective, diffusion and source terms, Gaussian quadratures, with account for the surface curvature, coordinate transformations using “serendipian” elements, are briefly described.

Keywords:

discontinuous Galerkin Method, basic functions, high order, supercomputer, verification, validation, high-lift wing

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