Model solution reliability is shown to be important for applications, where the computational method should accommodate a wide range of flow conditions through each model run without failure through instability or excessive run times. Such difficulties are linked to the use of poor assumptions in the derivation of models, in particular those neglecting energy solutions and the proper treatment of gradient discontinuities and shocks. Finite integral methods are introduced as a formal extension of longstanding traditional hydraulic analysis, leading through Control Element Lifetime Locus (CELL) Integral analysis to a new set of fundamental balance equations, the Full Hydraulic equations. These are then formulated for hydraulic streamtube analysis and discretised for separate numerical solutions for momentum and energy balances. Case studies for steady flow are referenced, where CELL energy balances improve solution robustness through a variable weighting scheme, accelerating convergence in comparison with widely used fixed weighting Upstream Differencing and Central Differencing schemes. A standard dambreak case study is then used to show the same robust system also copes with severe unsteady flow discontinuities, even while Courant Numbers are varied by orders of magnitude.

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