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S25 Métodos Numéricos |
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Title:
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ANALYTICAL SOLUTION OF THE LID DRIVEN CAVITY PROBLEM FOR REYNOLDS NUMBER TENDING TOWARDS ZERO
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Summary :
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VERY SLOW FLOW ARE TYPICAL FOR CASE WHERE THE VISCOSITY IS VERY HIGH. IN THIS CASE THE ASYMPTOTIC REYNOLDS NUMBER IS ZERO AND THE NAVIER-STOKES EQUATION ARE SIMPLIFIED TO LINEAR FORM, DENOMINATED IN THE LITERATURE AS STOKES PROBLEM. WHEN USED THE STREAM-FUNCTION ONLY FORMULATION IN A BI-DIMENSIONAL GEOMETRY, THE NAVIER-STOKES EQUATION TURN IN THE BIHARMONIC PROBLEM.
THE LID DRIVEN CAVITY PROBLEM IS A COMMON THEORETICAL TEST PROBLEM FOR COMPARISON OF DIFFERENT NUMERICAL METHODS. IN THE CASE OF REYNOLDS NUMBER TENDING TOWARDS ZERO AND RECTANGULAR GEOMETRY THE LITERATURE IS POOR IN ANALYTICAL SOLUTIONS THAT CAN BE USED AS BENCHMARK.
IN THE PRESENT WORK, THE GENERALISED INTEGRAL TRANSFORM TECHNIQUE(GITT), FOR YOUR NATURE ANALYTIC, TRANSFORM THE PARTIAL DIFFERENTIAL EQUATION IN A ORDINARY DIFFERENTIAL EQUATION SYSTEM, WHICH MAYBE SOLVED ANALYTICALLY VIA EIGENSYSTEM STRATEGY.
FORMAL ANALYTICAL SOLUTION AND RESULTS FOR THE STREAMFUNCTION IN DIFFERENT POSITIONS OF THE CAVITY ARE ILLUSTRATED.
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Author :
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Pérez Guerrero, Jesús Salvador
Pimentel, LuizClaudio Gomes
Ramos, Rogerio 0
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Paper View :
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