The potential 14C (carbon-14, radiocarbon) flux from disposal of 14C containing waste into air is compared with the natural 14C emanation rate from soil in order to put the 14C hazard potential from disposal of this waste in perspective with the 14C exposure from cosmogenic origin. Chemical corrosion of neutron irradiated metals, steel and Zircaloy, is bounded by diffusion of water through a thermodynamically stable metal-oxide layer and dissolution of this metal-oxide in a nuclear plant. Many countries process radioactive waste for disposal using cementitious materials, an acknowledged end-point management technique for this waste. The metal-oxides are also stable when these waste forms are embedded in cementitious materials. The 14C release rate from this Zircaloy at these alkaline and reducing conditions is comparable to the natural 14C emanation rate from soil into air. Neutron irradiated graphite and spent ion exchange resins are chemically inert and therefore other release mechanisms need to be assumed. Radiolytic corrosion is used to determine the 14C release rate from this graphite. Moreover, ion exchange—with ingressing anionic species that have a higher affinity than contained anionic 14C—is proposed as a release mechanism for these resins.

The numerical simulations for the blood flow in arteries by high order accurate schemes have a wide range of applications in medical engineering. The blood flow model admits the steady state solutions, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order finite volume weighted essentially non-oscillatory (WENO) scheme, which preserves the steady state solutions and maintains genuine high order accuracy for general solutions. The well-balanced property is obtained by a novel source term reformulation and discretisation, combined with well-balanced numerical fluxes. Extensive numerical experiments are carried out to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

In this study, we propose a high order well-balanced weighted compact nonlinear (WCN) scheme for the gas dynamic equations under gravitational fields. The proposed scheme is an extension of the high order WCN schemes developed in (S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321). For the purpose of maintaining the exact steady state solution, the well-balanced technique in (Y. Xing, C.-W Shu, J. Sci. Comput. 54 (2013) 645-662) is employed to split the source term into two terms. The proposed scheme can maintain the isothermal equilibrium solution exactly, genuine high order accuracy and resolve small perturbations of the hydrostatic balance state on the coarse meshes. Furthermore, in order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact schemes with local characteristic projections are used to construct different WCN schemes. Several representative one- and two-dimensional examples are simulated to demonstrate the good performance of the proposed schemes.

In this study, a numerical framework of the high order well-balanced weighted compact nonlinear (WCN) schemes is proposed for the shallow water equations based on the work in [S. Zhang, S. Jiang, C.-W Shu, J. Comput. Phys. 227 (2008) 7294-7321]. We employ a special splitting technique for the source term proposed in [Y. Xing, C.-W Shu, J. Comput. Phys. 208 (2005) 206-227] to maintain the exact C-property, which can be proved theoretically. In the meantime, the genuine high order accuracy of the numerical scheme can be observed successfully, and small perturbation of the stationary state can be resolved and evolved well. In order to capture the strong discontinuities and large gradients, the fifth-order upwind weighted nonlinear interpolations together with the fourth/sixth order cell-centered compact scheme are used to construct different WCN schemes. In addition, the local characteristic projections are considered to further restrain the potential numerical oscillations. A variety of representative one- and two-dimensional examples are tested to demonstrate the good performance of the proposed schemes.

This paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

In 2011 the IRSN conducted several assessments of atmosphericradioactive releases due to the Fukushima Daiichi NPP accident (March11, 2011) and of their impact on Japan’s terrestrial environment.They were based on the IRSN’s emergency management tools and onthe abundant information and technical data gradually publishedin Japan. According to these assessments, the main release phaselasted from March 12 to 25, 2011 and impacted Japanese land in twoevents, the first on 15 and 16 March, in which the main radioactivedeposits were formed, and the second from March 20 to 23, whichwas less significant. The highest amounts of radioactive deposits werefound in an area extending upwards of several tens of kilometersnorthwest of the plant. Lower amounts were discontinuously scatteredin an area extending up to over 250 km away. Initially composedmainly of short-lived radionuclides, the deposits’ activity sharplydecreased in the subsequent weeks. Since the summer of 2011, cesium-134and cesium-137 have become the residual deposits’ main components.According to IRSN estimates, in the absence of protection, the dosesdue to exposure to the radioactive plume during the atmosphericrelease phase may have been potentially higher for people who remainedin coastal areas up to several tens of kilometers north and southof the damaged plant. Thereafter, people living up to 50 km northwestof the plant, outside the 20-km emergency evacuation zone, were potentiallymost vulnerable to residual radioactive deposits over time.

We consider the Euler equations for compressible fluidsin a nozzle whose cross-section is variable and may contain discontinuities.We view these equations as a hyperbolic system in nonconservative formand investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [J. Math. Pures Appl.74 (1995) 483–548].Observing that the entropy equality has a fully conservative form,we derive a minimum entropy principle satisfied by entropy solutions.We then establish the stability of a class of numerical approximations for this system.