ABSTRACT (talk by T. Fara)We present a model simulating human body temperature when the extremities (such as hands or feet) are subject to extreme cold, possibly leading to hypothermia. The model involves (1) a PDE for the temperature in the extremity and (2) a reduced/lumped model of temperature in the body core. More specifically, (1) is a parabolic PDE with a nonlinear term modeling the tissue-vascular energy exchange similar to that derived by homogenization by Deuflhard and Hochmuth, and (2) is a constrained, nonlinear ODE. Phenomenologically, the model accounts for (i) the influence of warmed arterial blood on the extremity, (ii) the effect of cooling through the skin on the blood in the microvasculature, (iii) the resulting cooling of the venous blood and (iv) its impact back on the core temperature. Our model also describes (v) the body's attempt to control the loss of heat in the core during hypothermic crisis by vasoconstriction of the microvasculature. Our model is discretized, and the talk will describe our recent progress on the analysis of the numerical model, to be illustrated by simulations. This is joint work with M.Peszynska.

ABSTRACT (talk by J. Lily) Real-world simulations of ocean and atmosphere dynamics can take days to weeks of wall-clock time to complete even on leadership-class high performance computing systems. Many models use explicit time-stepping schemes, so their performance is limited by the CFL condition, which places a bound on the largest admittable time-step in terms of the size of the spatial discretization and, in the case of the shallow water equations, the gravity wave speed. Here, we present a Runge-Kutta type time-stepping scheme that has been optimized, in the CFL sense, specifically for the shallow water equations. We show that this new scheme, FB-RK(3,2), takes time-steps between 1.6 and 2.8 times larger than a comparable scheme. Next, we adapt this CFL optimized scheme to a local time-stepping (LTS) framework and implement the new LTS scheme (FB-LTS) in the Department of Energy ocean model, MPAS-Ocean. Within MPAS-Ocean, we test the performance of FB-LTS in a real-world test case simulating hurricane Sandy, showing that FB-LTS is 2.2 times faster than an existing LTS scheme, and 8.2 times faster than RK4.