A gas-kinetic BGK scheme for the two- and three-dimentional compressible flow /
In this thesis, the development of a robust and accurate numerical flow solver for the two- and three-dimensional compressible flow is of major interest. The underlying numerical scheme that is used to construct this so-called solver for the compressible flow is the gas-kinetic BGK (Bhatnagaar-Gross...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
Gombak, Selangor :
Kulliyyah of Engineering, International Islamic University Malaysia,
2010
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| Subjects: | |
| Online Access: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
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| Summary: | In this thesis, the development of a robust and accurate numerical flow solver for the two- and three-dimensional compressible flow is of major interest. The underlying numerical scheme that is used to construct this so-called solver for the compressible flow is the gas-kinetic BGK (Bhatnagaar-Gross-Krook), which is based on the collisional Boltzmann model. In this study, the algorithm for the gas-kinetic BGK flow solver is firstly developed to simulate two-dimensional compressible flow which includes the inviscid, laminar and turbulent realms of the flow. Subsequently, the developed algorithm is extended to three-dimensional compressible inviscid flow. All of the numerical treatments that are applied to solve the model equations of the flows are implemented via the finite difference approach. In such approach, the convection flux terms are discretized by a semi-discrete finite difference method, where the resulting inviscid flux functions are approximated by the BGK scheme. As for the diffusion flux terms, they are discretized by a second-order central difference scheme. A two-equation turbulence model of a combined k-ε / k-ω SST (Shear-Stress-Transport) model is used to provide the required Reynolds stresses to resolve the turbulent flow. To achieve higher-order spatial accuracy, the cell interface primitive flow variables are reconstructed by the use of MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) interpolation method coupled with a minmod limiter. For advancing the solutions to another time level, an explicit-type time integration method known as the modified fourth-order Runge-Kutta is employed in the flow solver to compute steady-state solution. In order to validate the solver and at the same time investigate its computational characteristics, several flow problems belonging to the two- and three-dimensional compressible flows are specifically chosen to be numerically analyzed. Developed solver for the two-dimensional compressible inviscid flow is tested with three typical flow problems, namely, supersonic channel flow, supersonic wedge cascade, and circular arc bump. In addition, four hypersonic test cases are also solved for the inviscid flow to test numerical shock instabilities which comprise the double Mach reflection, blunt body, axisymmetric blunt body and flow passing a 15o ramp problems. As for the two-dimensional compressible laminar flow, the following four test cases are used: 7.5o compression corner, laminar flat plate, hypersonic flow past a 24o compression ramp and hypersonic flow around a blunt body. Likewise, for the two-dimensional compressible turbulent flow, the four test cases chosen are the transitional flat plate, turbulent flat plate, RAE2822 airfoil, and Sajben diffuser. When extended to three-dimensions, the solver is used to predict four typical flow problems; namely, 10o cone at Mach 2.35, normal shock at Mach 1.3, supersonic wedge flow, and channel with a circular arc bump. For all these test cases, the numerical results are compared with available analytical, experimental and published numerical results from literature. These test cases show that the developed solver is robust, accurate and better than the central difference with TVD (Total Variation Diminishing), Steger-Warming FVS (Flux Vector Splitting) and Roe's FDS (Flux Difference Splitting) schemes, especially at high speed flow computations where the BGK scheme does not experience any shock instability as supported by the results published in this thesis. |
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| Item Description: | ''A thesis submitted in fulfilment of the requirement for the degree of Doctor of Philosophy"--On t.p. Abstract in English and Arabic. |
| Physical Description: | xviii, 148 p. : ill. (some col.) ; 30 cm. |
| Bibliography: | Includes bibliographical references (leaves 137-143). |