High order stiffly stable methods for ordinary differential equations

Supported in part by contract U.S. AEC AT(11-1) 1469 and in part by National Science Foundation grant NSF-GJ-217.

Optimal stiffly stable methods for ordinary differential equations,

"COO-1469-0164."

NORDSIECK FORMS OF STIFFLY-STABLE ADAMS-TYPE CYCLIC METHODS THAT ARE INSENSITIVE TO STEP-SIZE CHANGES

In this paper we determine a matrix S and a vector l for stiffly-stable Adams-type cyclic methods that are insensitive to step size changes by using the definition of equivalent methods, (see, e.g. [l]), in the Nordsieck notation. The elements S and l, written in a parametric form, permit us to represent in Nordsieck form the methods that were constructed in [7] and the new methods that satisfy the above properties.

A note on the non-existence of multivalue A-stable methods of order greater than two /

Bibliography: leaf 3.

Concerning the stability of BDF methods

We present an analysis of A0-stability of BDF methods and proof that zero-stable BDF methods are A0-stable using the Schur-Cohn criterion. With this result we have that zero-stable BDF methods are stiffly-stable. © 2008 American Institute of Physics.

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder at Re = 200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed. to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number.

Regularization of time-varying descriptor systems by the asvd

We study linear variable coefficient control problems in descriptor form. Based on a behaviour approach and the general theory for linear differential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system.

Isotopic fingerprints in surficial waters : Stable isotope methods applied in hydrogeological studies

The driving force behind this study has been the need to develop and apply methods for investigating the hydrogeochemical processes of significance to water management and artificial groundwater recharge. Isotope partitioning of elements in the course of physicochemical processes produces isotopic variations to their natural reservoirs. Tracer property of the stable isotope abundances of oxygen, hydrogen and carbon has been applied to investigate hydrogeological processes in Finland. The work described here has initiated the use of stable isotope methods to achieve a better understanding of these processes in the shallow glacigenic formations of Finland. In addition, the regional precipitation and groundwater records will supplement the data of global precipitation, but as importantly, provide primary background data for hydrological studies. The isotopic composition of oxygen and hydrogen in Finnish groundwaters and atmospheric precipitation was determined in water samples collected during 1995 2005. Prior to this study, no detailed records existed on the spatial or annual variability of the isotopic composition of precipitation or groundwaters in Finland. Groundwaters and precipitation in Finland display a distinct spatial distribution of the isotopic ratios of oxygen and hydrogen. The depletion of the heavier isotopes as a function of increasing latitude is closely related to the local mean surface temperature. No significant differences were observed between the mean annual isotope ratios of oxygen and hydrogen in precipitation and those in local groundwaters. These results suggest that the link between the spatial variability in the isotopic composition of precipitation and local temperature is preserved in groundwaters. Artificial groundwater recharge to glaciogenic sedimentary formations offers many possibilities to apply the isotopic ratios of oxygen, hydrogen and carbon as natural isotopic tracers. In this study the systematics of dissolved carbon have been investigated in two geochemically different glacigenic groundwater formations: a typical esker aquifer at Tuusula, in southern Finland and a carbonate-bearing aquifer with a complex internal structure at Virttaankangas, in southwest Finland. Reducing the concentration of dissolved organic carbon (DOC) in water is a primary challenge in the process of artificial groundwater recharge. The carbon isotope method was used to as a tool to trace the role of redox processes in the decomposition of DOC. At the Tuusula site, artificial recharge leads to a significant decrease in the organic matter content of the infiltrated water. In total, 81% of the initial DOC present in the infiltrated water was removed in three successive stages of subsurface processes. Three distinct processes in the reduction of the DOC content were traced: The decomposition of dissolved organic carbon in the first stage of subsurface flow appeared to be the most significant part in DOC removal, whereas further decrease in DOC has been attributed to adsorption and finally to dilution with local groundwater. Here, isotope methods were used for the first time to quantify the processes of DOC removal in an artificial groundwater recharge. Groundwaters in the Virttaankangas aquifer are characterized by high pH values exceeding 9, which are exceptional for shallow aquifers on glaciated crystalline bedrock. The Virttaankangas sediments were discovered to contain trace amounts of fine grained, dispersed calcite, which has a high tendency to increase the pH of local groundwaters. Understanding the origin of the unusual geochemistry of the Virttaankangas groundwaters is an important issue for constraining the operation of the future artificial groundwater plant. The isotope ratios of oxygen and carbon in sedimentary carbonate minerals have been successfully applied to constrain the origin of the dispersed calcite in the Virttaankangas sediments. The isotopic and chemical characteristics of the groundwater in the distinct units of aquifer were observed to vary depending on the aquifer mineralogy, groundwater residence time and the openness of the system to soil CO2. The high pH values of > 9 have been related to dissolution of calcite into groundwater under closed or nearly closed system conditions relative to soil CO2, at a low partial pressure of CO2.