A study of numerical methods for hyperbolic conservation laws with stiff source terms

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated

Chemical aging of m-xylene secondary organic aerosol: laboratory chamber study

Secondary organic aerosol (SOA) can reside in the atmosphere for a week or more. While its initial formation from the gas-phase oxidation of volatile organic compounds tends to take place in the first few hours after emission, SOA can continue to evolve chemically over its atmospheric lifetime. Simulating this chemical aging over an extended time in the laboratory has proven to be challenging. We present here a procedure for studying SOA aging in laboratory chambers that is applied to achieve 36 h of oxidation. The formation and evolution of SOA from the photooxidation of m-xylene under low-NO_x conditions and in the presence of either neutral or acidic seed particles is studied. In SOA aging, increasing molecular functionalization leads to less volatile products and an increase in SOA mass, whereas gas- or particle-phase fragmentation chemistry results in more volatile products and a loss of SOA. The challenge is to discern from measured chamber variables the extent to which these processes are important for a given SOA system. In the experiments conducted, m-xylene SOA mass, calculated under the assumption of size-invariant particle composition, increased over the initial 12–13 h of photooxidation and decreased beyond that time, suggesting the existence of fragmentation chemistry. The oxidation of the SOA, as manifested in the O:C elemental ratio and fraction of organic ion detected at m/z 44 measured by the Aerodyne aerosol mass spectrometer, increased continuously starting after 5 h of irradiation until the 36 h termination. This behavior is consistent with an initial period in which, as the mass of SOA increases, products of higher volatility partition to the aerosol phase, followed by an aging period in which gas- and particle-phase reaction products become increasingly more oxidized. When irradiation is stopped 12.4 h into one experiment, and OH generation ceases, minimal loss of SOA is observed, indicating that the loss of SOA is either light- or OH-induced. Chemical ionization mass spectrometry measurements of low-volatility m-xylene oxidation products exhibit behavior indicative of continuous photooxidation chemistry. A condensed chemical mechanism of m-xylene oxidation under low-NO_x conditions is capable of reproducing the general behavior of gas-phase evolution observed here. Moreover, order of magnitude analysis of the mechanism suggests that gas-phase OH reaction of low volatility SOA precursors is the dominant pathway of aging in the m-xylene system although OH reaction with particle surfaces cannot be ruled out. Finally, the effect of size-dependent particle composition and size-dependent particle wall loss rates on different particle wall loss correction methods is discussed

Star Formation in Cluster Galaxies at 0.2<z<0.55

The rest frame equivalent width of the [OII]3727 emission line, W(OII), has been measured for cluster and field galaxies in the CNOC redshift survey of rich clusters at 0.2<z<0.55. Emission lines of any strength in cluster galaxies at all distances from the cluster centre, out to 2R_{200}, are less common than in field galaxies. The mean W(OII) in cluster galaxies more luminous than M_r^k<-18.5 + 5\log h (q_o=0.1) is 3.8 \pm 0.3 A (where the uncertainty is the 1 sigma error in the mean), significantly less than the field galaxy mean of 11.2 \pm 0.3 A. For the innermost cluster members (R<0.3R_{200}), the mean W(OII) is only 0.3 \pm 0.4 A. Thus, it appears that neither the infall process nor internal tides in the cluster induce detectable excess star formation in cluster galaxies relative to the field. The colour-radius relation of the sample is unable to fully account for the lack of cluster galaxies with W(OII)>10 A, as expected in a model of cluster formation in which star formation is truncated upon infall. Evidence of supressed star formation relative to the field is present in the whole cluster sample, out to 2 R_{200}, so the mechanism responsible for the differential evolution must be acting at a large distance from the cluster centre, and not just in the core. The mean star formation rate in the cluster galaxies with the strongest emission corresponds to an increase in the total stellar mass of less than about 4% if the star formation is due to a secondary burst lasting 0.1 Gyr.Comment: aasms4 latex, 3 postscript figures, accepted for publication in ApJ Letters. Also available at http://astrowww.phys.uvic.ca/~balogh

Blackbody radiation in \kappa-Minkowski spacetime

We have computed the black body radiation spectra in $\kappa-$Minkowski space-time, using the quantum mechanical picture of massless scalar particles as well as effective quantum field theory picture. The black body radiation depends on how the field theory (and thus how the $\kappa-$Poincar\'e algebra) handles the ordering effect of the noncommutative space-time. In addition, there exists a natural momentum cut-off of the order $\kappa$, beyond which a new real mode takes its shape from a complex mode and the old real mode flows out to be a new complex mode. However, the new high momentum real mode should not be physical since its contributions to the black-body radiation spoils the commutative limit.Comment: 22pages, No figure, some corrections, to appear in Phys. Rev.

Hypersonic blunt body computations including real gas effects

The recently developed second-order explicit and implicit total variation diminishing (TVD) shock-capturing methods of the Harten and Yee, Yee, and van Leer types in conjunction with a generalized Roe's approximate Riemann solver of Vinokur and the generalized flux-vector splittings of Vinokur and Montagne for two-dimensional hypersonic real gas flows are studied. A previous study on one-dimensional unsteady problems indicated that these schemes produce good shock-capturing capability and that the state equation does not have a large effect on the general behavior of these methods for a wide range of flow conditions for equilibrium air. The objective of this paper is to investigate the applicability and shock resolution of these schemes for two-dimensional steady-state hypersonic blunt body flows. The main contribution of this paper is to identify some of the elements and parameters which can affect the convergence rate for high Mach numbers or real gases but have negligible effect for low Mach number cases for steady-state inviscid blunt body flows