MÉTODO CE/SE COM FUNÇÕES DE BASE POLINOMIAL DE SEGUNDA ORDEM PARA AS EQUAÇÕES DE SAINT VENANT UNIDIMENSIONAIS
DOI:
https://doi.org/10.26512/ripe.v2i12.21343Keywords:
Método CE/SE. Equações de Saint Venant. Polinômio de Taylor de 2a ordem.Abstract
O método dos elementos de conservação espaço-tempo e elementos de solução (CE/SE) é um método multidimensional robusto e acurado proposto por Chang em 1991. Fundamentado na resolução de leis de conservação, tal método é caracterizado por explorar, de modo conjunto, as formas integrais e diferenciais das leis de conservação. Apresenta-se, neste artigo, o desenvolvimento de um novo esquema CE/SE explícito para a solução das equações de Saint Venant unidimensionais, utilizando funções de base polinomiais de segunda ordem. Diferentemente dos esquemas tradicionais compostos por quatro variáveis de marcha, na presente formulação, as variáveis dinâmicas são aproximadas localmente por um polinômio de Taylor de segunda ordem, de modo que as equações resultantes são constituídas por seis incógnitas. As relações pertinentes à s duas variáveis adicionais são obtidas combinando-se as equações de continuidade e quantidade de movimento. Para demonstrar a acurácia, eficiência e robustez do método, problemas de ruptura de barragem, escoamentos subcríticos e transcríticos são simulados numericamente. Os resultados comprovam que o esquema proposto possui alta habilidade em capturar choques e descontinuidades.
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