Publicación: A NUMERICAL METHOD FOR A HEAT CONDUCTION MODEL IN A DOUBLE-PANE WINDOW
Fecha
2022
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AXIOMS
Resumen
IN THIS ARTICLE, WE PROPOSE A ONE-DIMENSIONAL HEAT CONDUCTION MODEL FOR A DOUBLE-PANE WINDOW WITH A TEMPERATURE-JUMP BOUNDARY CONDITION AND A THERMAL LAGGING INTERFACIAL EFFECT CONDITION BETWEEN LAYERS. WE CONSTRUCT A SECOND-ORDER ACCURATE FINITE DIFFERENCE SCHEME TO SOLVE THE HEAT CONDUCTION PROBLEM. THE DESIGNED SCHEME IS MAINLY BASED ON APPROXIMATIONS SATISFYING THE FACTS THAT ALL INNER GRID POINTS HAS SECOND-ORDER TEMPORAL AND SPATIAL TRUNCATION ERRORS, WHILE AT THE BOUNDARY POINTS AND AT INTER-FACIAL POINTS HAS SECOND-ORDER TEMPORAL TRUNCATION ERROR AND FIRST-ORDER SPATIAL TRUNCATION ERROR, RESPECTIVELY. WE PROVE THAT THE FINITE DIFFERENCE SCHEME INTRODUCED IS UNCONDITIONALLY STABLE, CONVERGENT, AND HAS A RATE OF CONVERGENCE TWO IN SPACE AND TIME FOR THE L?-NORM. MOREOVER, WE GIVE A NUMERICAL EXAMPLE TO CONFIRM OUR THEORETICAL RESULTS.
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UNCONDITIONAL NUMERICAL METHOD, HEAT CONDUCTION, FINITE DIFFERENCE METHOD, DOUBLE-PANE
