A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems

2008 ◽  
Vol 10 (3) ◽  
pp. 227-244 ◽  
Author(s):  
Olaf Kolditz ◽  
Jens-Olaf Delfs ◽  
Claudius Bürger ◽  
Martin Beinhorn ◽  
Chan-Hee Park

In this paper we present an object-oriented concept for numerical simulation of multi-field problems for coupled hydrosystem analysis. Individual (flow) processes modelled by a particular partial differential equation, i.e. overland flow by the shallow water equation, variably saturated flow by the Richards equation and saturated flow by the groundwater flow equation, are identified with their corresponding hydrologic compartments such as land surface, vadose zone and aquifers, respectively. The object-oriented framework of the compartment approach allows an uncomplicated coupling of these existing flow models. After a brief outline of the underlying mathematical models we focus on the numerical modelling and coupling of overland flow, variably saturated and groundwater flows via exchange flux terms. As each process object is associated with its own spatial discretisation mesh, temporal time-stepping scheme and appropriate numerical solution procedure. Flow processes in hydrosystems are coupled via their compartment (or process domain) boundaries without giving up the computational necessities and optimisations for the numerical solution of each individual process. However, the coupling requires a bridging of different temporal and spatial scales, which is solved here by the integration of fluxes (spatially and temporally). In closing we present three application examples: a benchmark test for overland flow on an infiltrating surface and two case studies – at the Borden site in Canada and the Beerze–Reusel drainage basin in the Netherlands.


2007 ◽  
Vol 04 (02) ◽  
pp. 299-333 ◽  
Author(s):  
D. ZEIDAN ◽  
A. SLAOUTI ◽  
E. ROMENSKI ◽  
E. F. TORO

We outline an approximate solution for the numerical simulation of two-phase fluid flows with a relative velocity between the two phases. A unified two-phase flow model is proposed for the description of the gas–liquid processes which leads to a system of hyperbolic differential equations in a conservative form. A numerical algorithm based on a splitting approach for the numerical solution of the model is proposed. The associated Riemann problem is solved numerically using Godunov methods of centered-type. Results show the importance of the Riemann problem and of centered schemes in the solution of the two-phase flow problems. In particular, it is demonstrated that the Slope Limiter Centered (SLIC) scheme gives a low numerical dissipation at the contact discontinuities, which makes it suitable for simulations of practical two-phase flow processes.


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