Numerical Study of Singular and Delta Shock Solutions Using a Large Time Step Method

We illustrate recently proposed large time step method for hyperbolic conservation laws. In the scalar case, it was proved earlier that if the approximate solutions converge boundedly, then they converge to the entropy solution. The main goal of this paper is to consider the large time step method for several systems of hyperbolic conservation laws. We compute approximate solutions to Riemann problems for three genuinely nonlinear one-dimensional systems (the Keyfitz-Kranzer system, the isentropic generalized Chaplygin gas dynamics equations, and the isentropic gas dynamics equations for polytropic gases with vanishing pressure). Besides approximating solutions that contain shocks and rarefaction waves, the focus is on approximating solutions which contain singular and delta shocks

Testing of intergranular and pitting corrosion in sensitized welded joints of austenitic stainless steel

Pitting corrosion resistance and intergranular corrosion of the austenitic stainless steel X5Cr Ni18-10 were tested on the base metal, heat affected zone and weld metal. Testing of pitting corrosion was performed by the potentiodynamic polarization method, while testing of intergranular corrosion was performed by the method of electrochemical potentiokinetic reactivation with double loop. The base metal was completely resistant to intergranular corrosion, while the heat affected zone showed a slight susceptibility to intergranular corrosion. Indicators of pitting corrosion resistance for the weld metal and the base metal were very similar, but their values are significantly higher than the values for the heat affected zone. This was caused by reduction of the chromium concentration in the grain boundary areas in the heat affected zone, even though the carbon content in the examined stainless steel is low (0.04 wt. % C)

Passivation behaviour of Alloy 31 (UNS N08031) in polluted phosphoric acid at different temperatures

The influence of temperature (20–80 °C) and chloride concentration (0.06–0.42 wt.% KCl) on the electrochemical behaviour of the UNS N08031 was studied in 40 wt.% polluted phosphoric acid solution. Passivation behaviour was investigated by using potentiostatic tests at different potentials. From the linear regions of the log i vs. log t transients, the parameter n was obtained. The results showed that the applied potential hardly affects on the passivation rate n. However, n values decreased when temperature increased. The values of n demonstrated that the passive film formed on Alloy 31 was compact and highly protective.The authors express their gratitude to the MAEC of Spain (PCI Mediterraneo C/8196/07, C/018046/08, D/023608/09 and D/030177/10), to Programa de Apoyo a la Investigacion y Desarrollo de la UPV (PAID-06-09) and to the Generalitat Valenciana (GV/2011/093) for the financial support and to Dr. Asuncion Jaime for her translation assistance.Escrivá Cerdán, C.; Blasco Tamarit, ME.; García García, DM.; García Antón, J.; Guenbour, A. (2012). Passivation behaviour of Alloy 31 (UNS N08031) in polluted phosphoric acid at different temperatures. Corrosion Science. 56:114-122. https://doi.org/10.1016/j.corsci.2011.11.014S1141225

Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments

Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor

Effect of temperature on passive film formation of UNS N08031 Cr-Ni alloy in phosphoric acid contaminated with different aggressive anions

tThe influence of temperature and the effect of aggressive anions on the electrochemical behaviour of UNSN08031 stainless steel in a contaminated phosphoric acid solution were evaluated. Stabilisation of thepassive film was studied by potentiodynamic polarisation curves, potentiostatic tests, electrochemicalimpedance spectroscopy (EIS) measurements, Mott Schottky analysis and X-ray photoelectron spec-troscopy (XPS). The stability of the passive film was found to decrease as temperature increases. The filmformed on the stainless steel surface was a n-type semiconductor and the XPS spectrum revealed thepresence of fluoride ions.Authors express their gratitude to the Ministry of Education of Spain (MHE2011-00202) for its financial support during the stay at University of Manchester, to MAEC of Spain (PCI Mediterraneo C/8196/07, C/018046/08, D/023608/09 and D/030177/10) and to the Generalitat Valenciana (GV/2011/093) for the financial support. The authors would also like to acknowledge the support of the School of Materials at the University of Manchester for providing analytical and technical support for the study.Escrivá Cerdán, C.; Blasco Tamarit, ME.; García García, DM.; García Antón, J.; Akid, R.; Walton, J. (2013). Effect of temperature on passive film formation of UNS N08031 Cr-Ni alloy in phosphoric acid contaminated with different aggressive anions. Electrochimica Acta. 111:552-561. https://doi.org/10.1016/j.electacta.2013.08.040S55256111

Properties of solutions in semi-hyperbolic patches for unsteady transonic small disturbance equations

We consider a two-dimensional Riemann problem for the unsteady transonic small disturbance equation resulting in diverging rarefaction waves. We write the problem in self-similar coordinates and we obtain a mixed type (hyperbolic-elliptic) system. Resolving the one-dimensional discontinuities in the far field, where the system is hyperbolic, and using characteristics, we formulate the problem in a semi-hyperbolic patch that is between the hyperbolic and the elliptic regions. A semi-hyperbolic patch is known as a region where one family out of two nonlinear families of characteristics starts on a sonic curve and ends on a transonic shock. We obtain existence of a smooth local solution in this semi-hyperbolic patch and we prove various properties of global smooth solutions based on a characteristic decomposition using directional derivatives

Large Time Step and Overlapping Grids for Conservation Laws

One focus of this dissertation is to construct a large time step Finite Volume Method for computing numerical solutions to hyperbolic systems of conservation laws. We also consider a method of overlapping spatial grids for which variants have proved to be an important consideration in large scale applications. In practice we often run into grids which have a fairly large range of cell sizes -- some cells may be relatively large compared to others which may be significantly smaller. For traditional finite volume methods, the smallest spatial cell size dictates the time step size limit when employing explicit time marching. Moreover, if a solution is obtained as a limit from a sequence of approximations which use exceedingly irregular girds, the limit solution may not even be a proper weak solution. The large time step method we propose here addresses both of these problems. We prove approximate solutions obtained are stable, and when convergent will always converge to a weak solution, regardless of relative grid cell sizes. Overlapping grids arise often in practice in order to discretized very complicated flow domains. One problem when grids overlap is how to identify a single valued approximation. A second issue is how to interface overlapping grids in such a way to obtain a conservative scheme. The method we propose here addresses both these issues. We identify a single valued approximate solution which employs overlapping spatial grids, and we prove its limit is a weak solution. Moreover, we show the method satisfies the maximum principle and is therefore stable. Chapter one is an introduction to the theory of hyperbolic conservation laws. In chapter two we introduce the finite volume method, approximate Riemann problem solvers, and we establish the Lax-Wendroff Theorem for the multidimensional algorithm. In chapter three we present our large time step method and establish the theoretical results noted above. Numerical examples are also given in this chapter. In the last chapter we present our overlapping grid method. The theoretical results indicated above are proved and several numerical examples are presented.Mathematics, Department o

Analysis of a Spacetime Discontinuous Galerkin Method for Systems of Conservation Laws

65 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.The focus of this dissertation is analysis of a causal spacetime discontinuous Galerkin (CSDG) method for one-dimensional hyperbolic systems of conservation laws. The CSDG method is based on causal spacetime discretizations, and the Galerkin basis herewith consists of piecewise constant functions. The method can be used on layered as well as on unstructured spacetime grids, and is well-suited for adaptive meshing and parallelization. Its formulation is consistent with the weak formulation of conservation laws and it naturally suggests a discrete version of the Lax entropy condition. The CSDG method is an explicit method, that is, a direct element-by-element solution procedure is possible. We investigate existence, uniqueness and continuous dependence on the initial data of a CSDG solution for general hyperbolic systems of conservation laws with Lipschitz continuous spatial flux function. We prove that if a CSDG solution exists, then it must satisfy discrete entropy inequalities. Our main result is for genuinely nonlinear Temple class systems. We show that given a causal spacetime mesh, a unique CSDG solution satisfying local Riemann invariant bounds exists. This enables us to prove convergence of the CSDG method to a weak solution which obeys certain entropy inequalities.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD