TY - CHAP
T1 - Energy inequalities and outflow boundary conditions for the navier-stokes equations
AU - Saito, Norikazu
AU - Sugitani, Yoshiki
AU - Zhou, Guanyu
N1 - Funding Information:
We thank Professors K. Takizazawa and H. Suito who brought the subject to our attention. We also thank Dr. T. Kashiwabara for his valuable suggestions. This work is supported by Japan Science and Technology CorporationJST,Core Research for Evolutional Science and TechnologyCREST,and Japan Society for the Promotion of Science London JSPS KAKENHI (23340023,15H03635,15K13454).
Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016
Y1 - 2016
N2 - Artificial boundary conditions play important roles in numerical simulation of real-world flow problems. A typical example is a class of outflow boundary conditions for blood flow simulations in large arteries. The common outflow boundary conditions are a prescribed constant pressure or traction,a prescribed velocity profiles,and a free-traction (do-nothing) conditions. However,the flow distribution and pressure field are unknown and cannot be prescribed at the outflow boundary in many simulations. Moreover,with those boundary conditions,we are unable to obtain energy inequalities. This disadvantage may cause numerical instability in unstationary 3D simulations. In this paper,we examine some outflow boundary conditions for the Navier-Stokes equations from the viewpoint of energy inequalities. Further,we propose an energy-preserving unilateral condition and review mathematical results including the well-posedness,variational inequality formulations,and finite element approximations.
AB - Artificial boundary conditions play important roles in numerical simulation of real-world flow problems. A typical example is a class of outflow boundary conditions for blood flow simulations in large arteries. The common outflow boundary conditions are a prescribed constant pressure or traction,a prescribed velocity profiles,and a free-traction (do-nothing) conditions. However,the flow distribution and pressure field are unknown and cannot be prescribed at the outflow boundary in many simulations. Moreover,with those boundary conditions,we are unable to obtain energy inequalities. This disadvantage may cause numerical instability in unstationary 3D simulations. In this paper,we examine some outflow boundary conditions for the Navier-Stokes equations from the viewpoint of energy inequalities. Further,we propose an energy-preserving unilateral condition and review mathematical results including the well-posedness,variational inequality formulations,and finite element approximations.
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U2 - 10.1007/978-3-319-40827-9_24
DO - 10.1007/978-3-319-40827-9_24
M3 - Chapter
AN - SCOPUS:84992365707
T3 - Modeling and Simulation in Science, Engineering and Technology
SP - 307
EP - 317
BT - Modeling and Simulation in Science, Engineering and Technology
PB - Springer Basel
ER -