DIFFERENCE SOLUTIONS OF SHALLOW-WATER EQUATION

THE QUASI-LINEAR PARTIAL DIFFERENTIAL EQUATIONS KNOWN AS THE SHALLOW-WATER EQUATIONS DESCRIBE THE FLOW OF WATER IN OPEN CHANNELS OR OVER SLOPING PLANES /OVERLAND FLOW/. BECAUSE NO ANALYTIC SOLUTION EXISTS FOR THESE EQUATIONS, FINITE-DIFFERENCE METHODS MUST BE USED TO OBTAIN SOLUTIONS. FORMULATION OF FINITE-DIFFERENCE SCHEMES INVOLVES CONSIDERATION OF THE CONVERGENCE OF THE FINITE-DIFFERENCE SOLUTIONS TO THE TRUE SOLUTION OF THE EQUATION. A THEORETICAL EXAMINATION OF THE APPROXIMATION OF SEVERAL DIFFERENCE OPERATORS, BOTH IMPLICIT AND EXPLICIT, IS PRESENTED AND THE STABILITY OF THESE SCHEMES IS EXAMINED EMPIRICALLY FOR FLOW OVER A PLANE WITH CRITICAL DEPTH DOWNSTREAM BOUNDARY CONDITION AND A ZERO INFLOW UPSTREAM BOUNDARY CONDITION. A FINITE-DIFFERENCE SCHEME BASED ON THE METHOD OF CHARACTERISTICS WAS FOUHD TO BE SATISFACTORY IN MANY CASES. EXPLICIT METHODS WERE FOUND TO BE NOT SUITABLE FOR THIS PROBLEM EXCEPT IN SOME SPECIAL CASES. REFERENCE' DIFFERENT SOLUTIONS OF SHALLOW-WATER EQUATION, JAMES A. LIGGETT & DAVID A. WOOLHISER, JOURNAL OF THE ENGINEERING MECHANICS DIVISION, ASCE, VOL. 93, NO EM 2, PROC PAPER 5189, PP 39-71, APRIL 1967.

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  • Supplemental Notes:
    • Vol 93, No EM2, PP 39-71, 14 FIG, 1 TAB, 1 REF
  • Publication Date: 1967-4

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  • Accession Number: 00204086
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Jul 28 1994 12:00AM