The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
type: Item
instance of: scholarly article
title: The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
zbMATH Open document ID: 0931.76080
published in: Journal of Computational Physics
publication date: 2000-02-28T00:00:00Z
review text: The purpose of this work is to show how the hydrodynamic equations can be differenced compatibly so that they obey the conservation properties. In particular, it is shown how conservation of total energy can be utilized as an intermediate device to achieve this goal for the equations of fluid dynamics written in Lagrangian form, and with a staggered spatial placement of variables for any number of dimensions and in any coordinate system. For staggered spatial variables it is shown how the momentum equation and the specific internal energy equation can be derived from each other in a simple and generic manner by use of the conservation of total energy. This allows for the specification of forces that can be of an arbitrary complexity, such as those derived from an artificial viscosity or subzonal pressures. These forces originate only in discrete form; nonetheless, the change in internal energy caused by them is still completely determined. The procedure given here is compared to the ``method of support operators'', to which it is closely related. Difficulties with conservation of momentum, volume, and entropy are also discussed, together with the proper treatment of boundary conditions and differencing with respect to time. \(\copyright\) Academic Press.
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 76M20
zbMATH DE Number: 1240717
zbMATH Keywords: Lagrangian form of hydrodynamic equations
zbMATH Keywords: Sedov blast wave problem
zbMATH Keywords: conservation of volume
zbMATH Keywords: conservation of entropy
zbMATH Keywords: conservation of mass
zbMATH Keywords: method of support operators
zbMATH Keywords: staggered spatial variables
zbMATH Keywords: momentum equation
zbMATH Keywords: internal energy equation
zbMATH Keywords: conservation of momentum
zbMATH Keywords: boundary conditions
zbMATH Keywords: differencing
author: Edward J. Caramana
author: Donald E. Burton
author: Mikhail Shashkov
author: Paul P. Whalen
MaRDI profile type: Publication
OpenAlex ID: W2108182238
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DOI: 10.1006/JCPH.1998.6029
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description: scientific article; zbMATH DE number 1240717