Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.     

Mathematical modeling of PCB bioaccumulation in Perna viridis

In the present work, we built a mathematical model of polychlorinated biphenyl (PCB) bioaccumulation in Perna viridis, namely, a one-compartment model with a time dependent incorporation rate R (μg g⁻¹ lipid per ppb water per day), with positive substrate cooperativity as the underlying physical mechanism. The temporal change of the PCB concentration Q (μg g⁻¹ lipid) in the soft tissues of the mussel depends on the competition of the input rate RW and the output rate kQ, where W is the concentration of PCB in water (ppb water) and k is the elimination rate (per day). From our experimental data, k=0.181±0.017 d⁻¹. The critical concentration in water W_c for positive substrate cooperativity was found to be 2.4 ppb. Below W_c, R is a constant. For a water concentration of 0.5 ppb Aroclor 1254, R=24.0±2.4 μg g⁻¹ lipid ppb⁻¹ d⁻¹. Above W_c, positive substrate cooperativity comes into effect and R becomes a function of time and dependent on the concentration Q in a form R=γQ/(Q+δ). This is the case for a water concentration of 5 ppb Aroclor 1254, where γ=15.1 μg g⁻¹ lipid ppb⁻¹ d¹ and δ≈200 μg g⁻¹ lipid. From this model, the uptake is exponentially increasing when the PCB concentration in the mussel is small compared to 200 μg g⁻¹ lipid, and hyperbolically increasing when the concentration is large compared to 200 μg g⁻¹ lipid, which are consistent with the experimental data. The model is useful for understanding the true processes taking place during the bioaccumulation and for risk assessment with higher confidence. Future experimental data which challenge the present model are anticipated and in fact desirable for improvement and perfection of the model.     

Burrowing responses of the short-neck clam Ruditapes philippinarum to sediment contaminants

The burrowing responses of a common tropical bivalve, the short-neck clam Ruditapes philippinarum, to cadmium (Cd)-spiked sediment, variations of sediment grain size and natural sediments collected from 15 locations in Hong Kong's inshore waters were investigated through a series of laboratory tests. Results showed that the burrowing response exhibited a negative relationship with an increase in Cd concentration in the spiked sediments. The level of Cd was also found to be directly proportional to the percent mortality of the clam. However, there was no significant difference (p>0.05) in the time elapsed for the clam to burrow into sediments with different grain size composition. The elapsed time for 50% of the test clams to burrow into the sediment (ET₅₀) over a period of 48 h was calculated for the sediment samples collected from the 15 locations. Results of ANOVA showed significant difference (p<0.05) among the sediment samples. Tukey's multiple comparison test revealed two groups of sediments: group 1 containing 3 sediment samples collected from Victoria Harbour and group 2 containing 12 samples obtained from other coastal areas of Hong Kong. The ET₅₀ value for group 1 sediments was found to be greater than 2880 min whilst the ET₅₀ for group 2 sediments had a mean of 173.9 min. Agglomerative classification of the sediment samples, based on metal content (As, Cd, Cr, Cu, Ni, Pb, Zn), also showed two similar groups, suggesting that the ET₅₀ values were correlated with the metal level of the sediment samples. Group 1 sediments collected from Victoria Harbour had greater concentrations of Cd, Cr, Cu, Ni and Zn as compared to that in group 2. The present study demonstrated that high metal content in the sediment tends to inhibit the burrowing responses of the clam and that there is potential to develop the burrowing responses of R. philippinarum as a sublethal sediment toxicity test.     

Effects of heavy metals on the survival and feeding behaviour of the sandy shore scavenging gastropod Nassarius festivus (Powys)

The effects of Cu, Cd, Zn and Cr on the survival and feeding behaviour of the sandy shore scavenging gastropod Nassarius festivus were compared. The 96-h LC₅₀ for Cu, Cd, Zn and Cr were 0.36, 1.52, 1.76 and 36.9 mg l⁻¹, respectively. Four sublethal concentrations of each metal plus a control were prepared and the snails were exposed to experimental solutions for 96 h. Feeding behaviour was studied after the snails were starved for five days. As compared with the control, the number of individuals feeding was significantly reduced by exposure to 0.05 mg l⁻¹ Cu, 0.2 mg l⁻¹ Zn, 0.5 mg l⁻¹ Cd and 5 mg l⁻¹ Cr. The time spent feeding was greater for individuals exposed to greater concentrations of Zn and Cd but no effect was found for Cu and Cr. Chemoreception of food was studied by placing the snails at a fixed distance of 15 cm from the bait. The success rate of reaching the bait was less for individuals exposed to Cr but no effect was found for Zn, Cu or Cd. The time required for an individual to reach the bait decreased as the concentration of Zn increased. In contrast, a longer time was required for individuals exposed to Cr whereas the effect of Cd and Cu was insignificant. The potential of using feeding behaviour and chemoreception in contaminant evaluations is discussed.     

Wave propagation in layered media by time domain BEM

A time domain boundary element in a cylindrical co-ordinate system is developed for the analysis of wave propagation in a layered half-space. The field quantities (displacements and tractions) are expressed as products of Fourier series in the circumferential direction and as linear polynomials in the other spatial directions. An integral equation is written for each layer as an independent domain, and these equations are then assembled into a general equation by virtue of compatibility and equilibrium conditions between the interfaces. Examples of three-dimensional wave propagation in the layered half-spaces due to various forms of surface and inner-domain excitations are reported to demonstrate the accuracy and versatility of the method.     

Sodar observations of the stable lower atmospheric boundary layer at Barrow,Alaska

Events in the stably stratified lower atmospheric boundary layer within the first several hundreds of meters at Barrow, Alaska were recorded from 27 March to 5 April 1990 using an acoustic sounder (sodar), a tethered balloon, radiosondes, and an instrumented meteorological tower. These events include ground-based and low-level inversion layers, gravity waves, breaking waves, and multiple-layer structures. Even though these events are commonly found in a stable boundary layer, it is perhaps surprising to find them in such a slowly changing environment and over a terrain that is essentially devoid of immediate orographic influence.Visiting Scientist at Wave Propagation Laboratory, NOAA/ERL 325 Broadway, Boulder, CO, 80303, U.S.A.     

Transient elastodynamic analysis by time domain bem in cylindrical coordinates

A time domain boundary element in a cylindrical coordinate system is developed for the analysis of wave propagation in a half space. The integral formulation is based on Graffi's dynamic reciprocal theorem and Stokes' fundamental solutions. The field quantities (displacements and tractions) are expressed as products of Fourier series in the tangential direction and linear polynomials in the other spatial directions. Gaussian integration is used to integrate the non-singular parts of the integral equations, whereas the integration of the singular components, which are either of order 1/r or 1/r², is handled by special numerical schemes. In the time marching aspect, the field quantities are assumed to vary linearly in the temporal direction as well. Examples for wave propagation due to various forms of surface excitations are reported to demonstrate the accuracy of the method.     

A semi-analytical boundary element method for scattering of waves in a half space

A boundary element method using finite strip discretization is proposed to investigate the three-dimensional scattering behaviour of waves in a half space. The scatterers examined are an irregular surface and a cavity in a half space. The numerical examples demonstrate the remarkably good accuracy of the results and validate the application of the present method to solve three-dimensional scattering problems.     

Infinite layer for the analysis of a single pile

This paper proposes a solution for single pile embedded in layered soil. The soil is divided into a number of infinite layers and the displacement shape functions of the layer are given as a product of piecewise polynomial expansion along the depth and series expansions in radial as well as tangential directions. The pile is divided into a number of solid bar elements along its length and it deforms as a rigid section in the horizontal plane. The interaction between the two components can be treated in the standard manner. Typical examples of a single pile are presented to demonstrate the versatility and accuracy of the method.