Mesh generation and adaptive remeshing by genetic algorithms on transonic flow simulation

Abstract

In this paper, we mtroducc dúferent npplicntions of geneuc algonlhms on transontc ílow problems Tous a rcgulanz.auon proccss of unstructured meshes is proposed. From a startmg mesh. n new one ts built employmg gcneuc aJgorithms to nunun1z.ed a fitness function wb1ch is based on geometrlcal cond1oons Lhat allow to get better tbe quahty of tbe mesh and on error md1cators providing mfoonation about its dens1ty. Severa! Fitness functions are suggcsted depending on lhe propo cd objectives to obtnm a bel ter mesh, mcludmg dúf erenl geometrical considerations regardmg aren, penmeter, angles, etc., of the triangles and error measurements based on the denS1ty of the flu1d , the ma.cb number or bolb of them. Sorne companson criteria must be fixed in arder to analyze the quality of the mesbes. Toe control of lhe nades is done by bmary codes, assuming that they are equ1valent to the cbromosomes of the elements of a populauon. From thts population, tbe genetic laws lead to new ones by the selecllon, crossover and mutation between parent chromosomes. Th1s process 1s repeated till Lhe approXllnalc solution of the global optimum is found f or tbe fitness function. Toe parameters of reproducnon, crossover. mutatlon probabilities and s12e of the population must be analyzed to obta10 a robust algorithm. To1s wa.y, an adaptive finite element lS perfonned movmg nades far a good remeshing. Toe procedurc may be generalized to tbree-dimens1onal unstructured meshes by construction of layers of triangular prism. An extens1on of tbe methodology is suggested f or optimization problems over profile (design problem) with genetic algonthms. A transomc compressible fiow problem 1s studied for differeot mesh strateg1es, usmg a vers1on of non linear GMRES