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A higher-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows Nejat, Amir
Abstract
A fast implicit (Newton-Krylov) finite volume algorithm is developed for higher-order unstructured (cell-centered) steady-state computation of inviscid compressible flows (Euler equations). The matrix-free General Minimal Residual (GMRES) algorithm is used for solving the linear system arising from implicit discretization of the governing equations, avoiding expensive and complicated explicit computation of the higher-order Jacobian matrix. An Incomplete Lower-Upper factorization technique is employed as the preconditioning strategy and a first-order Jacobian as a preconditioning matrix. The solution process is divided into two phases: start-up and Newton iterations. In the start-up phase an approximate solution of the fluid flow is computed which includes most of the physical characteristics of the steady-state flow. A defect correction procedure is proposed for the start-up phase consisting of multiple implicit pre-iterations. At the end of the start-up phase (when the linearization of the flow field is accurate enough for steady-state solution) the solution is switched to the Newton phase, taking an infinite time step and recovering a semi-quadratic convergence rate (for most of the cases). A proper limiter implementation for higher-order discretization is discussed and a new formula for limiting the higher-order terms of the reconstruction polynomial is introduced. The issue of mesh refinement in accuracy measurement for unstructured meshes is revisited. A straightforward methodology is applied for accuracy assessment of the higher-order unstructured approach based on total pressure loss, drag measurement, and direct solution error calculation. The accuracy, fast convergence and robustness of the proposed higher-order unstructured Newton-Krylov solver for different speed regimes are demonstrated via several test cases for the 2nd, 3rd and 4th-order discretization. Solutions of different orders of accuracy are compared in detail through several investigations. The possibility of reducing the computational cost required for a given level of accuracy using high-order discretization is demonstrated.
Item Metadata
Title |
A higher-order accurate unstructured finite volume Newton-Krylov algorithm for inviscid compressible flows
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2007
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Description |
A fast implicit (Newton-Krylov) finite volume algorithm is developed for higher-order unstructured
(cell-centered) steady-state computation of inviscid compressible flows (Euler
equations). The matrix-free General Minimal Residual (GMRES) algorithm is used for solving
the linear system arising from implicit discretization of the governing equations, avoiding
expensive and complicated explicit computation of the higher-order Jacobian matrix. An
Incomplete Lower-Upper factorization technique is employed as the preconditioning strategy
and a first-order Jacobian as a preconditioning matrix. The solution process is divided
into two phases: start-up and Newton iterations. In the start-up phase an approximate
solution of the fluid flow is computed which includes most of the physical characteristics
of the steady-state flow. A defect correction procedure is proposed for the start-up phase
consisting of multiple implicit pre-iterations. At the end of the start-up phase (when the
linearization of the flow field is accurate enough for steady-state solution) the solution is
switched to the Newton phase, taking an infinite time step and recovering a semi-quadratic
convergence rate (for most of the cases). A proper limiter implementation for higher-order
discretization is discussed and a new formula for limiting the higher-order terms of the
reconstruction polynomial is introduced. The issue of mesh refinement in accuracy measurement
for unstructured meshes is revisited. A straightforward methodology is applied for
accuracy assessment of the higher-order unstructured approach based on total pressure loss,
drag measurement, and direct solution error calculation. The accuracy, fast convergence
and robustness of the proposed higher-order unstructured Newton-Krylov solver for different
speed regimes are demonstrated via several test cases for the 2nd, 3rd and 4th-order
discretization. Solutions of different orders of accuracy are compared in detail through several
investigations. The possibility of reducing the computational cost required for a given
level of accuracy using high-order discretization is demonstrated.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-01-28
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080717
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.