Hidrológiai Közlöny 1995 (75. évfolyam)

2. szám - Gáspár Csaba–Józsa János–Simbierowicz, Pawel: Új szemléletmód a numerikus hidraulikában. IV. Áramlási és transzportfolyamatok Langrange-féle modellezése egyenlőtlen hálók használatával

86 HIDROLÓGIAI KÖZLÖNY 1995. 75. ÉVF. 2. SZ^JVI Raviart, P.A. (1986) "Partiele Numerical Models in Fluid Dynamics". In: Numerical Methods for Fluid Dynamics 11. (ed. by K. W. Morton, M. G. Baines). Clarendon Press, Oxford. Thompson, M.C., Ferziger, J.H. (1989) "An Adaptive MultigridTechnique for the Incompressible Navier-Stokes Equations". J. Comput. Physics, Vol. 82. Shen, H.T., Yapa, P.D., Petroski, M.E. (1987) "A Simulation Model for Oil Slick Transport in Lakes". Water Resour. Res. Vol. 23, No. 10. A kézirat beérkezett: 1992 augusztus 24. Közlésre elfogadva: 1994. április 5. GÁSPÁR CSABA Oki. matematikus (1978), egyetemi doktor (1982), a matematikai tud. kandidátusa (1994), főiskolai tud. főmunkatárs. Szakmai működését részletesebben a Hidrológiai Közlöny 1988. évi 5. sz. 288. oldalán ismertettük. JÓZSA JÁNOS Oki. mérnök (1981), egyetemi doktor(1991), a műszaki tud. kandidátusa (1993), műegyetemi adjunktus. Szakmai működését részletesebben a Hidrológiai Közlöny 1988. évi 1. sz. 23. oldalán ismertettük. SIMBIEROWICZ Old. matematikus-mémök (Budapesti Műszaki Egyetem, 1985), a Finnországi Műszaki Kutatási Központ tudoPAWEL mányos munkatársa. New Approach in Numerical Hydraulics IV.Lagrangian Modeling of Flow and Transport Processes with the Help of Irregular Grids Gáspár, Cs.-Józsa, J.-Simbierowicz, P. Abstract: A növel approach to numerical hydraulics is presented in four successive. These are entitled: I.Irregular grids, their generation and first applications. II.Difference schemes and multigrid methods on irregular grids. III.Modeling wind induced currents in shallow lakes with the help of irregular grids. IV.Lagrangian modeling of flow and transport processes with the help of irregular grids. The "növel approach" consists essentially of abandoning the equidistant finite-difference philosophy and replacing it with the more generál QT grid which provides irregular subdivision in space, is orthogonal, can be generated in a flexible way and is based on the recursively defined, systematic subdivision of and initial square. The analysis can thus be focused on the subtantially important subregions. When using the QT-grids, the grid and mátrix philosophy is replaced by graphs. An additional important feature of the new approach is the multigrid technique. Thanks to the attractive properties of the QT-grids coupled with multigrid techniques i.e. the high speed of computation and the high degree of flexibility, the proposed new method is a competitive alternative to the earlier computational methods. In this fmal paper, the method is applied to Lagrangian modeling i.e. to moving coordinate systems. In this way, the convective derivativescan be eliminated, therefore a pure elliptic problem is to be solved in each time step. These subproblems are treated in separate quadtree grids generated by the Lagrangian points. The grid generation and the diseretisation is fast enough to be applied repeatedly in each time step. The approach is applied to the conservative transport problem as well as the Helmholz-Kelvin instability problem: note that the latter problem is highly nonlinear. Keywords: numerical hydraulics, flow modeling, grid, graph, multigrid, computational methods, Lagrangian modeling, Kelvin-Helmholz-problem.