Discontinuous solutions to hyperbolic systems under operator splitting

Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps solves exactly the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to pseudo acoustic waves and a non-physical stationary wave. The implications of these findings for the design of high-resolution computing schemes are discussed

Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics

A possible technique is explored for extending to multidimensional flows some of the upwind-differencing methods that are highly successful in the one-dimensional case. Emphasis is on the two-dimensional case, and the flow domain is assumed to be divided into polygonal computational elements. Inside each element, the flow is represented by a local superposition of elementary solutions consisting of plane waves not necessarily aligned with the element boundaries

The 'optimum' upwind advection on a triangular mesh

For advection schemes based on fluctuation splitting, a design criterion of optimizing the time step leads to linear schemes that coincide with those designed for least truncation error. A further stage of optimizing the time step using a nonlinear positivity criterion, leads to considerable further gains in resolution

Error estimates for cell-vertex solutions of the compressible Euler equations

The cell-vertex schemes due to Ni and Jameson, et al. have been subjected to a theoretical analysis of their truncation error. The analysis confirms the authors' claims for second-order accuracy on smooth grids, but shows that the same accuracy cannot be obtained on arbitrary grids. It is shown that the schemes have a unique generalization to axisymmetric flow that preserves the second-order accuracy

Development of non-dissipative numerical schemes for computational aeroacoustics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76586/1/AIAA-1993-3382-851.pd

Notes and Discussion Piece: Status of the Topeka Shiner in Iowa

The Topeka shiner Notropis topeka is native to Iowa, Kansas, Minnesota, Missouri, Nebraska, and South Dakota and has been federally listed as endangered since 1998. Our goals were to determine the present distribution and qualitative status of Topeka shiners throughout its current range in Iowa and characterize the extent of decline in relation to its historic distribution. We compared the current (2016–2017) distribution to distributions portrayed in three earlier time periods. In 2016–2017 Topeka shiners were found in 12 of 20 HUC10 watersheds where they occurred historically. Their status was classified as stable in 21% of the HUC10 watersheds, possibly stable in 25%, possibly recovering in 8%, at risk in 33%, and possibly extirpated in 13% of the watersheds. The increasing trend in percent decline evident in earlier time periods reversed, going from 68% in 2010–11 to 40% in the most recent surveys. Following decades of decline, the status of Topeka shiners in Iowa appears to be improving. One potential reason for the reversal in the distributional decline of Topeka shiners in Iowa is the increasing number of oxbow restorations. Until a standardized monitoring program is established for Iowa, periodic status assessments such as this will be necessary to chronicle progress toward conserving this endangered fish species

Unification of some advection schemes in two dimensions

The relationship between two approaches towards construction of genuinely two-dimensional upwind advection schemes is established. One of these approaches is of the control volume type applicable on structured cartesian meshes. It resulted in the compact high resolution schemes capable of maintaining second order accuracy in both homogeneous and inhomogeneous cases. Another one is the fluctuation splitting approach, which is well suited for triangular (and possibly) unstructured meshes. Understanding the relationship between these two approaches allows us to formulate here a new fluctuation splitting high resolution (i.e. possible use of artificial compression, while maintaining positivity property) scheme. This scheme is shown to be linearity preserving in inhomogeneous as well as homogeneous cases

5-Year survival of pediatric anterior cruciate ligament reconstruction with living donor hamstring tendon grafts

Background: It is well accepted that there is a higher incidence of repeat anterior cruciate ligament (ACL) injuries in the pediatric population after ACL reconstruction (ACLR) with autograft tissue compared with adults. Hamstring autograft harvest may contribute to the risk for repeat ACL injuries in this high functional demand group. A novel method is the use of a living donor hamstring tendon (LDHT) graft from a parent; however, there is currently limited research on the outcomes of this technique, particularly beyond the short term. Purpose/Hypothesis: The purpose was to determine the medium-term survival of the ACL graft and the contralateral ACL (CACL) after primary ACLR with the use of an LDHT graft from a parent in those aged less than 18 years and to identify factors associated with subsequent ACL injuries. It was hypothesized that ACLR with the use of an LDHT provides acceptable midterm outcomes in pediatric patients. Study Design: Case series; Level of evidence, 4. Methods: Between 2005 and 2014, 247 (of 265 eligible) consecutive patients in a prospective database, having undergone primary ACLR with the use of an LDHT graft and aged less than 18 years, were included. Outcomes were assessed at a minimum of 2 years after surgery including data on ACL reinjuries, International Knee Documentation Committee (IKDC) scores, and current symptoms, as well as factors associated with the ACL reinjury risk were investigated. Results: Patients were reviewed at a mean of 4.5 years (range, 24-127 months [10.6 years]) after ACLR with an LDHT graft. Fifty-one patients (20.6%) sustained an ACL graft rupture, 28 patients (11.3%) sustained a CACL rupture, and 2 patients sustained both an ACL graft rupture and a CACL rupture (0.8%). Survival of the ACL graft was 89%, 82%, and 76% at 1, 2, and 5 years, respectively. Survival of the CACL was 99%, 94%, and 86% at 1, 2, and 5 years, respectively. Survival of the ACL graft was favorable in patients with Tanner stage 1-2 at the time of surgery versus those with Tanner stage 3-5 at 5 years (87% vs 69%, respectively; hazard ratio, 3.7; P = .01). The mean IKDC score was 91.7. A return to preinjury levels of activity was reported by 59.1%. Conclusion: After ACLR with an LDHT graft from a parent in those aged less than 18 years, a second ACL injury (ACL graft or CACL injury) occurred in 1 in 3 patients. The 5-year survival rate of the ACL graft was 76%, and the 5-year survival rate of the CACL was 86%. High IKDC scores and continued participation in sports were maintained over the medium term. Importantly, there was favorable survival of the ACL graft in patients with Tanner stage 1-2 compared with patients with Tanner stage 3-5 over 5 years. Patients with Tanner stage 1-2 also had a significantly lower incidence of second ACL injuries over 5 years compared with those with Tanner stage 3-5, occurring in 1 in 5 patients. Thus, an LDHT graft from a parent is an appropriate graft for physically immature children

A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77007/1/AIAA-1989-95-623.pd

Evaluation of Euler Fluxes for Hypersonic Flow Computations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76462/1/AIAA-33735-324.pd