Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows

Feng Xiao, Ryosuke Akoh, Satoshi Ii

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

Following our previous paper on a novel finite volume formulation for computing flows of any Mach number, we present the multi-dimensional extension of the method in this paper. Treating two kinds of averages, which are generically called 'moments' and defined as the volume integrated average (VIA) and the surface integrated average (SIA) in this paper, as the prognostic variables makes the present method different from the conventional finite volume method where only VIA is the basic variable. The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moment method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows. The numerical algorithm for multi-dimensions will be reported in this paper. Numerical experiments with flows of a wide range Mach numbers will be also presented.

Original languageEnglish
Pages (from-to)31-56
Number of pages26
JournalJournal of Computational Physics
Volume213
Issue number1
DOIs
Publication statusPublished - Mar 20 2006
Externally publishedYes

Fingerprint

compressible flow
incompressible flow
Compressible flow
Incompressible flow
Finite volume method
Mach number
moments
formulations
Method of moments
finite volume method
Experiments
projection
simulation

Keywords

  • Compressible and incompressible flows
  • Conservative scheme
  • Euler conservation laws
  • Multi-dimensional simulation
  • Pressure projection
  • Shock capturing
  • Unified method

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

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title = "Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows",
abstract = "Following our previous paper on a novel finite volume formulation for computing flows of any Mach number, we present the multi-dimensional extension of the method in this paper. Treating two kinds of averages, which are generically called 'moments' and defined as the volume integrated average (VIA) and the surface integrated average (SIA) in this paper, as the prognostic variables makes the present method different from the conventional finite volume method where only VIA is the basic variable. The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moment method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows. The numerical algorithm for multi-dimensions will be reported in this paper. Numerical experiments with flows of a wide range Mach numbers will be also presented.",
keywords = "Compressible and incompressible flows, Conservative scheme, Euler conservation laws, Multi-dimensional simulation, Pressure projection, Shock capturing, Unified method",
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T2 - Multi-dimensional version for compressible and incompressible flows

AU - Xiao, Feng

AU - Akoh, Ryosuke

AU - Ii, Satoshi

PY - 2006/3/20

Y1 - 2006/3/20

N2 - Following our previous paper on a novel finite volume formulation for computing flows of any Mach number, we present the multi-dimensional extension of the method in this paper. Treating two kinds of averages, which are generically called 'moments' and defined as the volume integrated average (VIA) and the surface integrated average (SIA) in this paper, as the prognostic variables makes the present method different from the conventional finite volume method where only VIA is the basic variable. The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moment method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows. The numerical algorithm for multi-dimensions will be reported in this paper. Numerical experiments with flows of a wide range Mach numbers will be also presented.

AB - Following our previous paper on a novel finite volume formulation for computing flows of any Mach number, we present the multi-dimensional extension of the method in this paper. Treating two kinds of averages, which are generically called 'moments' and defined as the volume integrated average (VIA) and the surface integrated average (SIA) in this paper, as the prognostic variables makes the present method different from the conventional finite volume method where only VIA is the basic variable. The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moment method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows. The numerical algorithm for multi-dimensions will be reported in this paper. Numerical experiments with flows of a wide range Mach numbers will be also presented.

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KW - Pressure projection

KW - Shock capturing

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