Computer Simulations of Fluid Flow

The research project that was financed by the Ministry of Science, Education, and Sport of the Republic of Croatia (previous Ministry of Science and Technology) and that started in 1998 covered following areas:



We developed a computer program that implements numerous state of the art numerical schemes for one-dimensional and two-dimensional hyperbolic conservation laws. We proposed new finite difference numerical schemes for hyperbolic conservation law systems with geometrical source terms that are actually well-balanced ENO and WENO schemes. We proved that these new schemes when applied to shallow water equations and sediment transport equations have the exact conservation property. Also we obtained balancing in upwind schemes for open channel flows, for channels with general, i.e, also for nonprismatic and nonrectangular geometry. We solved the complete problem of mathematical modeling, numerical modeling and computer simulation for open-channel flow, flooding and sediment transport, and we applied it to:



We also solved the complete problem of mathematical modeling, numerical modeling and computer simulation for nonstationary liquid-gas mixture flow in a pipeline consisting of pipes, reservoirs, valves, air chambers, surge tanks, pumps, turbines etc. The final computer model covers waterhammer and cavitation phenomena. We applied genetic algorithms (GA) to problems of optimal control of valve and pump operations in pipelines, shape design in turbomachinery and naval architecutre, and to model calibration problems. Figures present some of our results. All our code is object oriented, mostly C++, code, weather it is core code that implements numerical schemes or GUI code. We always apply extensive testing on classical test problems and we use OpenGL for all graphics in our computer program.

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