Simulation of 1D steady flow covers a wide range of practical applications, such as rivers, pipes and hydraulic structures. Various flow patterns coexist in such situations: free surface flows (supercritical, subcritical and hydraulic jump), pressurized flows as well as mixed flows. As a result, development of a unified 1D model for all the situations of interest in civil engineering remains challenging. In this paper, a fast universal solver for 1D continuous and discontinuous steady flows in rivers and pipes is set up and assessed. Developments are initiated from an original unified mathematical model using the Saint-Venant equations. Application of these equations, originally dedicated to free-surface flow, is extended to pressurized flow by means of the Preissmann slot model. In particular, an original negative slot is developed in order to handle sub-atmospheric pressurized flow. Next, the full unsteady model is simplified under the assumption of steadiness and reformulated into a single pseudo-unsteady differential equation. The derived pseudo-unsteady formulation aims at keeping the hyperbolic feature of the equation. Stability analysis of the differential equation suggests a unique splitting for the finite volume scheme whatever the flow conditions. The numerical scheme obtained is a universal Flux Vector Splitting which shows robustness and simplicity. Accuracy and performance of the new methodology is assessed by comparison with analytical and experimental results. Copyright © 2009 John Wiley & Sons, Ltd.
martes, 29 de diciembre de 2009
A fast universal solver for 1D continuous and discontinuous steady flows in rivers and pipes
Simulation of 1D steady flow covers a wide range of practical applications, such as rivers, pipes and hydraulic structures. Various flow patterns coexist in such situations: free surface flows (supercritical, subcritical and hydraulic jump), pressurized flows as well as mixed flows. As a result, development of a unified 1D model for all the situations of interest in civil engineering remains challenging. In this paper, a fast universal solver for 1D continuous and discontinuous steady flows in rivers and pipes is set up and assessed. Developments are initiated from an original unified mathematical model using the Saint-Venant equations. Application of these equations, originally dedicated to free-surface flow, is extended to pressurized flow by means of the Preissmann slot model. In particular, an original negative slot is developed in order to handle sub-atmospheric pressurized flow. Next, the full unsteady model is simplified under the assumption of steadiness and reformulated into a single pseudo-unsteady differential equation. The derived pseudo-unsteady formulation aims at keeping the hyperbolic feature of the equation. Stability analysis of the differential equation suggests a unique splitting for the finite volume scheme whatever the flow conditions. The numerical scheme obtained is a universal Flux Vector Splitting which shows robustness and simplicity. Accuracy and performance of the new methodology is assessed by comparison with analytical and experimental results. Copyright © 2009 John Wiley & Sons, Ltd.
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