We describe a strategy for detecting discontinuities and for limiting spurious oscillations near such discontinuities when solving hyperbolic systems of conservation laws by high-order discontinuous Galerkin methods. The approach is based on a strong superconvergence at the outflow boundary of each element in smooth regions of the flow. By detecting discontinuities in such variables as density or entropy, limiting may be applied only in these regions; thereby, preserving a high order of accuracy in regions where solutions are smooth. Several one-and two-dimensional flow problems illustrate the performance of these approaches.

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Synchronous gastric tumors that consist of both gastrointestinal stromal tumor (GIST) and adenocarcinoma are rare. We studied the clinicopathological and molecular characteristics of six cases containing both gastric adenocarcinoma and GIST. By means of immunohistochemical analysis, all GIST cells expressed CD117, CD34 and Dog1 in all six synchronous gastric adenocarcinomas with GIST, and in GIST alone. Sequencing analysis demonstrated that exon 11 c-kit mutations were present in two of six synchronous tumors and four of five GISTs. One of the two exon 11 c-kit mutations in synchronous adenocarcinomas with GISTs was an uncommon mutation of CTT > CCA at amino acid 576, and the other was a GTT deletion at amino acid 560. The mutation was a homozygous A > G mutation in exon 12 (amino acid 567) of PDGFR-α. We concluded that the exon 11 mutations were the most important in both cases of synchronous gastric adenocarcinoma with GIST and GIST alone. The mutation rate was higher in GIST alone than in synchronous adenocarcinoma with GIST.

We describe procedures to model transient shock interaction problems using discontinuous Galerkin methods to solve the compressible Euler equations. The problems are motivated by blast flows surrounding cannons with perforated muzzle brakes. The goal is to predict shock strengths and blast over pressure. This application illustrates several computational difficulties. The software must handle complex geometries. The problems feature strong interacting shocks, with pressure ratios on the order of 1000 as well as weaker precursor shocks traveling rearward that also must be accurately captured. These aspects are addressed using anisotropic mesh adaptation. A shock detector is used to control the adaptation and limiting. We also describe procedures to track projectile motion in the flow by a level-set procedure.

Non-equilibrium radiation measurements behind strong shock wave for simulated Martian atmosphere are presented in this paper. The shock wave is established in a hydrogen oxygen combustion driven shock tube. Timeresolved spectra of the Δv = 0 sequence of the B 2 Σ + → X 2 Σ + electronic transition of CN have been observed through optical emission spectroscopy (OES). A new method, which is based on fitting high resolution spectrum for rotational and vibrational temperatures measurement, is proposed to diagnose temperature distribution behind the shock wave. It is estimated that the current scheme has the maximum deviation less than 8% (1σ) for vibrational temperature measurement through detailed analysis of the influence of the uncertainties of spectroscopic constants and spectral resolution. Radiation structure of the shock layer, including induction, relaxation and equilibrium process, and corresponding rotational and vibrational temperatures are obtained through time gating OES diagnostics with sub-microsecond temporal resolution. The present extensive results will strongly benefit the reaction rate estimation and computational fluid dynamics (CFD) code validation in high enthalpy Mars reentry chemistry.