A study on the application of Navier-Stokes equations to the unstructured grid system (bibtex)
by Lee, Yong Hoon
Abstract:
The analysis of a preconditioned Navier-Stokes solver with an unstructured grid system has been performed to comprehend the numerical algorithm and techniques; the code has been evaluated by solving several test problems. To overcome the slow convergence problem in time marching scheme for the low mach number regime, a preconditioning method has been applied which changes governing equations by replacing time derivative term with artificial variables. Also, a dual time stepping method has been applied to solve unsteady problems. The unstructured grid system has been employed with the finite volume method which has a high degree of freedom in generating grid for complex geometry. The second-order upwind scheme using least-square gradient construction has been applied for a low numerical diffusion. Euler implicit method has been applied for the discretization of time derivative term. The point Gauss-Seidel(PGS) and the line Gauss-Seidel(LGS) have been used to solve linear system of equations. Finally, the convergence and the validity of the solution have been verified by solving several test problems. A wide range of flow problems from low mach number(M=0.001) laminar flow to supersonic(M=3) shock reflection has been used to verify the convergence and the accuracy of the solutions for both inviscid and viscous flow. Also the performance of the PGS and the LGS solvers has been compared. Computational results indicate that the LGS solver solves the problem faster because the maximum allowable CFL number for the LGS solver is higher than the maximum allowable CFL number for the PGS solver.
Reference:
Yong Hoon Lee, "A study on the application of Navier-Stokes equations to the unstructured grid system", Master's thesis, Ajou University, Suwon, Korea, 2010.
Bibtex Entry:
@mastersthesis{Lee2010MS,
    author = "Lee, Yong Hoon",
    title = "A study on the application of {Navier-Stokes} equations to the unstructured grid system",
    school = "Ajou University",
    address = "Suwon, Korea",
    year = "2010",
    month = aug,
    pdf = "http://www.dcollection.net/handler/ajou/000000010845",
    abstract = "The analysis of a preconditioned Navier-Stokes solver with an unstructured grid system has been performed to comprehend the numerical algorithm and techniques; the code has been evaluated by solving several test problems. To overcome the slow convergence problem in time marching scheme for the low mach number regime, a preconditioning method has been applied which changes governing equations by replacing time derivative term with artificial variables. Also, a dual time stepping method has been applied to solve unsteady problems. The unstructured grid system has been employed with the finite volume method which has a high degree of freedom in generating grid for complex geometry. The second-order upwind scheme using least-square gradient construction has been applied for a low numerical diffusion. Euler implicit method has been applied for the discretization of time derivative term. The point Gauss-Seidel(PGS) and the line Gauss-Seidel(LGS) have been used to solve linear system of equations. Finally, the convergence and the validity of the solution have been verified by solving several test problems. A wide range of flow problems from low mach number(M=0.001) laminar flow to supersonic(M=3) shock reflection has been used to verify the convergence and the accuracy of the solutions for both inviscid and viscous flow. Also the performance of the PGS and the LGS solvers has been compared. Computational results indicate that the LGS solver solves the problem faster because the maximum allowable CFL number for the LGS solver is higher than the maximum allowable CFL number for the PGS solver.",
}
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