MAST solution of irrotational flow problems in 2D domains with strongly unstructured triangular meshes

A new methodology for the solution of irrotational 2D flow problems in domains with strongly unstructured meshes is presented. A fractional time step procedure is applied to the original governing equations, solving consecutively a convective prediction system and a diffusive corrective system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system, of the order of the number of computational cells. A MArching in Space and Time (MAST) approach is applied for the solution of the convective prediction step. The major advantages of the model, as well as its ability to maintain the solution monotonicity even in strongly irregular meshes, are briefly described. The algorithm is applied to the solution of diffusive shallow water equations in a simple domain

Monotonic solution of heterogeneous anisotropic diffusion problems

Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of each side with the "anisotropic" circumcentre of each final triangle. A structure of the flux across the control volume sides similar to the standard Galerkin Finite Element scheme is derived. A special treatment of the flux computation, mainly based on edge swaps of the initial mesh triangles, is proposed in order to obtain a stiffness M-matrix system that guarantees the monotonicity of the solution. The proposed scheme is tested using several literature tests and the results are compared with analytical solutions, as well as with the results of other algorithms, in terms of convergence order. Computational costs are also investigate

Extensible Wind Tower

The diffusion of wind energy generators is restricted by their strong landscape impact. The PERIMA project is about the development of an extensible wind tower able to support a wind machine for several hundred kW at its optimal working height, up to more than 50 m. The wind tower has a telescopic structure, made by several tubes located inside each other with their axis in vertical direction. The lifting force is given by a jack-up system confined inside a shaft, drilled below the ground level. In the retracted tower configuration, at rest, tower tubes are hidden in the foundation of the telescopic structure, located below the ground surface, and the wind machine is the only emerging part of the system. The lifting system is based on a couple of oleodynamic cylinders that jack-up a central tube connected to the top of the tower by a spring, with a diameter smaller than the minimum tower diameter and with a length a bit greater than the length of the extended telescopic structure. The central tube works as plunger and lifts all telescopic elements. The constraint between the telescopic elements is ensured by special parts, which are kept in traction by the force of the spring and provide the resisting moment. The most evident benefit of the proposed system is attained with the use of a two-blade propeller, which can be kept horizontal in the retracted tower configuration

Comparison of different 2nd order formulations for the solution of the 2D groundwater flow problem over irregular triangular meshes

Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper, a new MHFE formulation is proposed for the solution of the 2D linear groundwater flow problem over domain discretized by means of triangular irregular meshes. The numerical results of the modified MHFE procedure are compared with the results of a modified 2 nd spatial approximation order Finite Volume (FV2) formulation [2], as well as with the results given by the standard MHFE method. The FV2 approach is equivalent to the standard MHFE approach in the case of isotropic medium and regular or mildly irregular mesh, but has a smaller number of unknowns and better matrix properties. In the case of irregular mesh, an approximation is proposed to maintain the superior matrix properties of the FV2 approach, with the consequent introduction of a small error in the computed solution. The modified MHFE formulation is equivalent to the standard MHFE approach in both isotropic and heterogeneous medium cases, using regular or irregular computational meshes, but has a smaller number of unknowns for given mesh geometr

Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes

Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The transport problem is solved applying a prediction/correction procedure. The prediction step analytically solves the convective/reactive components in the context of a MAST Finite Volume scheme. The correction step computes the anisotropic diffusive components in the context of a recently proposed Finite Elements scheme. Massa balance is locally and globally satisfied in all the solution steps. Convergence order and computational costs are investigated and model results are compared with literature on

Anisotropic potential of velocity fields in real fluids: Application to the MAST solution of shallow water equations

In the present paper it is first shown that, due to their structure, the general governing equations of uncompressible real fluids can be regarded as an "anisotropic" potential flow problem and closed streamlines cannot occur at any time. For a discretized velocity field, a fast iterative procedure is proposed to order the computational elements at the beginning of each time level, allowing a sequential solution element by element of the advection problem. Some closed circuits could appear due to the discretization error and the elements involved in these circuits could not be ordered. We prove in the paper that the total flux of these not ordered elements goes to zero by refining the computational mesh and that it is possible to order all the remaining elements by neglecting the minimum inter-element flux inside each circuit, with a very small resulting error.The methodology is then applied to the solution of the 2D shallow water equations. The governing Partial Differential Equations are discretized over a generally unstructured triangular mesh, which attains the generalised Delaunay property. Solution is obtained applying a prediction-correction time step procedure. The prediction problem is solved applying a MArching in Space and Time (MAST) procedure, where the computational elements are required to be ordered and explicitly solved. In the correction step, a large linear well-conditioned system is solved. Model results are compared with experimental data and other numerical literature results. Computational costs have been estimated and the convergence order has been investigated according to a known exact solution. © 2013 Elsevier Ltd

Discharge estimation combining flow routing and occasional measurements of velocity

A new procedure is proposed for estimating river discharge hydrographs during flood events, using only water level data at a single gauged site, as well as 1-D shallow water modelling and occasional maximum surface flow velocity measurements. One-dimensional diffusive hydraulic model is used for routing the recorded stage hydrograph in the channel reach considering zero-diffusion downstream boundary condition. Based on synthetic tests concerning a broad prismatic channel, the “suitable” reach length is chosen in order to minimize the effect of the approximated downstream boundary condition on the estimation of the upstream discharge hydrograph. The Manning’s roughness coefficient is calibrated by using occasional instantaneous surface velocity measurements during the rising limb of flood that are used to estimate instantaneous discharges by adopting, in the flow area, a two-dimensional velocity distribution model. Several historical events recorded in three gauged sites along the upper Tiber River, wherein reliable rating curves are available, have been used for the validation. The outcomes of the analysis can be summarized as follows: (1) the criterion adopted for selecting the “suitable” channel length based on synthetic test studies has proved to be reliable for field applications to three gauged sites. Indeed, for each event a downstream reach length not more than 500m is found to be sufficient, for a good performances of the hydraulic model, thereby enabling the drastic reduction of river cross-sections data; (2) the procedure for Manning’s roughness coefficient calibration allowed for high performance in discharge estimation just considering the observed water levels and occasional measurements of maximum surface flow velocity during the Correspondence to: G. Corato ([email protected]) rising limb of flood. Indeed, errors in the peak discharge magnitude, for the optimal calibration, were found not exceeding 5% for all events observed in the three investigated gauged sections, while the Nash-Sutcliffe efficiency was, on average, greater than 0.95. Therefore, the proposed procedure well lend itself to be applied for: (1) the extrapolation of rating curve over the field of velocity measurements (2) discharge estimations in different cross sections during the same flood event using occasional surface flow velocity measures carried out, for instance, by hand-held radar sensors