PDEModelica and Breathing in an Avalanche

This paper presents an updated version of Modelica language extension for partial differential equations (PDE) called PDEModelica and implementation of its support in OpenModelica. This support is limited to 1-dimensional problems and the first and second partial derivatives. PDEModelica is introduced by a string equation model and later by a real life model of respiration during a snow burial. This model describes CO​2​ advection and diffusion in snow described by advection-diffusion PDE. PDEModelica, PDE, avalanche survival

[1]  T. Crowley,et al.  O2 and CO2 Levels With the Black Diamond AVALUNG During Human Snow Burials Lasting Up to One Hour , 1998 .

[2]  W. Schiesser The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .

[3]  François E. Cellier,et al.  Support for Dymola in the Modeling and Simulation of Physical Systems with Distributed Parameters , 2008 .

[4]  M. Scholand,et al.  Normal oxygenation and ventilation during snow burial by the exclusion of exhaled carbon dioxide. , 2001, Wilderness & environmental medicine.

[5]  B. Tremper,et al.  Cause of Death in Avalanche Fatalities , 2007, Wilderness & environmental medicine.

[6]  Mauro Valt,et al.  Avalanche fatalities in the European Alps: long-term trends and statistics , 2016 .

[7]  R. Courant,et al.  On the Partial Difference Equations, of Mathematical Physics , 2015 .

[8]  Vincent Heuveline,et al.  PDE Modeling with Modelica via FMI Import of HiFlow3 C++ Components with Parallel Multi-core Simulations , 2014, Simul. Notes Eur..

[9]  L. Sieger,et al.  Work of Breathing into Snow in the Presence versus Absence of an Artificial Air Pocket Affects Hypoxia and Hypercapnia of a Victim Covered with Avalanche Snow: A Randomized Double Blind Crossover Study , 2015, PloS one.

[10]  Jirí Kofránek,et al.  Physiomodel - an integrative physiology in Modelica , 2015, 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[11]  Peter Fritzson,et al.  Principles of Object-Oriented Modeling and Simulation with Modelica 3.3: A Cyber-Physical Approach , 2014 .

[12]  J. Strikwerda Finite Difference Schemes and Partial Differential Equations , 1989 .