| dc.description.abstract | The thesis presents several studies on finite difference modelling of groundwater flow systems. The studies include:
(i) Development of an efficient computational algorithm for nonrectangular flow domains;
(ii) Comparative study of iterative methods for linear problems;
(iii) Comparative study of iterative methods for nonlinear problems;
(iv) Application of an aquifer–water table aquitard model for a regional problem; and
(v) Application of an aquifer–water table aquitard model for a well field problem.
The most powerful numerical method for solving groundwater flow problems, namely, the Strongly Implicit Procedure (SIP), is normally used with a superscribed rectangular computational region with dummy nodes outside the flow region. This is done in order to preserve the structure of the coefficient matrix of the finite difference equations to a specific pattern. However, this procedure wastes a lot of computer storage and time, and the wastage of storage becomes particularly important as SIP requires a larger storage than the other competitive methods.
A modified Strongly Implicit Procedure has been developed which eliminates the need for dummy nodes and is directly applicable for nonrectangular flow regions. It is shown that except for four types of boundary nodes, the classical SIP algorithm is directly applicable for nonrectangular regions also. The equations for these special types of boundary nodes are derived.
Algorithms of other iterative methods, namely, the Successive Over-Relaxation method (SOR), the Line Successive Over-Relaxation method (LSOR), the Alternating Direction Implicit method (ADI), the Modified Alternating Direction Implicit method (MADI) and the Line Alternating Direction Implicit method (LADI) have also been presented so as to be directly applicable for nonrectangular flow regions. The LADI method has not been used in groundwater literature earlier. The MADI method, which is a particular case of the LADI method, has, however, been used.
A comparative study of SOR, LSOR, ADI, MADI, LADI and SIP methods applied to six linear two-dimensional test problems is presented. The emphasis has been on the direct application of these methods for nonrectangular flow regions. The problems include homogeneous, nonhomogeneous and layered media, and homogeneous and nonhomogeneous anisotropic media, with mixed Dirichlet and Neumann conditions. The effect of relaxation or iteration parameters and variations in the rate of convergence and numerical fluctuations for different methods are studied. Based on the computational results, all the finite difference methods are graded for the above three aspects. It is found that from all considerations, except computer storage, SIP is the best method. For situations in which available computer storage is limited, guidelines are provided for the use of other methods depending on the nature of the problem.
Numerical fluctuations are of importance in solving unconfined flow problems as some nodes may get artificially dropped out of the computation. Thus, a need arises to look for methods which dampen these fluctuations if not eliminate them altogether. A comparative study of the Picard and the Newton iterative methods is made for nonlinear problems. Both the Picard and the Newton algorithms are associated with SIP, LADI and SOR methods for solving the linear equations in the iterative process, resulting in PSIP (Picard SIP), PLADI, PSOR, NSIP (Newton SIP), NLADI and NSOR methods. These methods are applied on two isotropic test problems with homogeneous and nonhomogeneous domains, with one of them designed as a critical problem with a zone of thin saturated thickness.
Aspects studied include sensitivity to relaxation or iteration parameters, rate of convergence and numerical fluctuations. It is found that numerical fluctuations (hence risk of artificial desaturation) in the PSIP method is a function of the number of iteration parameters, increasing with increase in the number of parameters. A four-parameter sequence is found to be the best for both the PSIP and the NSIP methods and use of a larger number of iteration parameters is not desirable. The PSIP and NSIP methods are vastly superior to the other methods discussed. Corrective measures are proposed for the PSIP method to avoid artificial desaturation without any significant reduction in the convergence rate.
A modified leaky aquifer model with an aquifer–water table aquitard system has been used for regional groundwater modelling of the 24,200 sq. km Vedavati River Basin covering parts of Karnataka and Andhra Pradesh in India. The basin is a typical crystalline hard rock area. In the model, the entire weathered and clayey zone above the deeper anisotropic fracture-aquifer is treated as a composite unconfined aquitard. The model is calibrated using regional water level observations over a period of one year. The calibrated model is used to obtain the regional distribution of safe yield over the basin and to identify regions of over-exploitation and maximum potential.
The regional model of the aquifer–water table aquitard system uses an approximate equation for the aquitard zone. A rigorous quasi three-dimensional numerical analysis of a well field problem in an anisotropic aquifer–water table aquitard system is made. The analysis treats the water table as an unknown boundary and considers storage release from the aquitard. The coupled aquifer–aquitard equations are solved in a two-level iteration process, involving separate inner iterations for both aquifer and aquitard zones. The SIP method is used for the aquifer while an iterative Thomas algorithm is used for the aquitard zone. The results are compared with two approximate numerical methods, which ignore the storage release in the aquitard. The numerical results are compared with analytical solutions which ignore the effect of water table decline. The vertical distribution of head in the aquitard is studied. | |
