Numerical calculations of two dimensional, unsteady transonic flows with circulation

The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data

On the application and extension of Harten's high resolution scheme

Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations

An extension of A-stability to alternating direction implicit methods

An alternating direction implicit (ADI) scheme was constructed by the method of approximate factorization. An A-stable linear multistep method (LMM) was used to integrate a model two-dimensional hyperbolic-parabolic partial differential equation. Sufficient conditions for the A-stability of the LMM were determined by applying the theory of positive real functions to reduce the stability analysis of the partial differential equations to a simple algebraic test. A linear test equation for partial differential equations is defined and then used to analyze the stability of approximate factorization schemes. An ADI method for the three-dimensional heat equation is also presented

Flux vector splitting of the inviscid equations with application to finite difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included

Alternating direction implicit methods for parabolic equations with a mixed derivative

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme

Impact of sequence variation in the ul128 locus on production of human cytomegalovirus in fibroblast and epithelial cells

The human cytomegalovirus (HCMV) virion envelope contains a complex consisting of glycoproteins gH and gL plus proteins encoded by the UL128 locus (UL128L): pUL128, pUL130, and pUL131A. UL128L is necessary for efficient infection of myeloid, epithelial, and endothelial cells but limits replication in fibroblasts. Consequently, disrupting mutations in UL128L are rapidly selected when clinical isolates are cultured in fibroblasts. In contrast, bacterial artificial chromosome (BAC)-cloned strains TB40-BAC4, FIX, and TR do not contain overt disruptions in UL128L, yet no virus reconstituted from them has been reported to acquire mutations in UL128L in vitro. We performed BAC mutagenesis and reconstitution experiments to test the hypothesis that these strains contain subtle mutations in UL128L that were acquired during passage prior to BAC cloning. Compared to strain Merlin containing wild-type UL128L, all three strains produced higher yields of cell-free virus. Moreover, TB40-BAC4 and FIX spread cell to cell more rapidly than wild-type Merlin in fibroblasts but more slowly in epithelial cells. The differential growth properties of TB40-BAC4 and FIX (but not TR) were mapped to single-nucleotide substitutions in UL128L. The substitution in TB40-BAC4 reduced the splicing efficiency of UL128, and that in FIX resulted in an amino acid substitution in UL130. Introduction of these substitutions into Merlin dramatically increased yields of cell-free virus and increased cell-to-cell spread in fibroblasts but reduced the abundance of pUL128 in the virion and the efficiency of epithelial cell infection. These substitutions appear to represent mutations in UL128L that permit virus to be propagated in fibroblasts while retaining epithelial cell tropism

Projected Spatiotemporal Dynamics of Drought under Global Warming in Central Asia

Drought, one of the most common natural disasters that have the greatest impact on human social life, has been extremely challenging to accurately assess and predict. With global warming, it has become more important to make accurate drought predictions and assessments. In this study, based on climate model data provided by the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP), we used the Palmer Drought Severity Index (PDSI) to analyze and project drought characteristics and their trends under two global warming scenarios—1.5 °C and 2.0 °C—in Central Asia. The results showed a marked decline in the PDSI in Central Asia under the influence of global warming, indicating that the drought situation in Central Asia would further worsen under both warming scenarios. Under the 1.5 °C warming scenario, the PDSI in Central Asia decreased first and then increased, and the change time was around 2080, while the PDSI values showed a continuous decline after 2025 in the 2.0 °C warming scenario. Under the two warming scenarios, the spatial characteristics of dry and wet areas in Central Asia are projected to change significantly in the future. In the 1.5 °C warming scenario, the frequency of drought and the proportion of arid areas in Central Asia were significantly higher than those under the 2.0 °C warming scenario. Using the Thornthwaite (TH) formula to calculate the PDSI produced an overestimation of drought, and the Penman–Monteith (PM) formula is therefore recommended to calculate the index

Are philosophers responsible for global warming?

Global warming has come about as a result of rapid population increase plus our whole modern way of life, all made possible by modern science. In order to tackle global warming successfully, we need a new kind of inquiry that gives intellectual priority to tackling problems of living over problems of knowledge. If we had had this new kind of inquiry fifty years ago, we might have begun to do something about global warming long ago, in the early 1960s, when Keeling first discovered that carbon dioxide was increasing in the atmosphere. Our long-standing failure to respond to global warming is in part due to our failure to develop a genuinely rigorous kind of inquiry devoted to helping us tackle our global problems, which is, in turn, a philosophical failure. Philosophers are responsible for global warming to the extent that they have failed to highlight this philosophical blunder inherent in academia in part responsible for our tardy response to global warming