Construction of high-order accuracy implicit residual smoothing schemes |
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Authors: | Ni Mingjiu Lecturer Doctor Xi Guang Wang Shangjin |
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Institution: | (1) School of Energy and Power Engineering, Xi'an Jiaotong University, 710049 Xi'an, P R China |
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Abstract: | Referring to the construction way of Lax-Wendroff scheme, new IRS (Implicit Residual Smoothing) schemes have been developed
for hyperbolic, parabolic and hyperparabolic equations. These IRS schemes have 2nd-order or 3rd-order time accuracy, and can
extend the stability region of basic explicit time-stepping scheme greatly and thus can permit higher CFL number in the calculation
of flow field. The central smoothing and upwind-bias smoothing techniques have been developed too. Based on one-dimensional
linear model equation, it has been found that the scheme is uncomditionally stable according to the von-Neumann analysis.
The limitation of Dawes' method, which has been applied in turbomachinery widespreadly, has been discussed on solving steady
flow and viscous flow. It is shown that stable solution of this method is not completely independent with the value of time
step. In the end, numerical results by using IRS schemes and Dawes' method as well as TVD (total variation diminishing) scheme
and four-stage Runge-Kutta technique are presented to verify the analytical conclusions.
Foundation item: Doctoral Education Foundation of National Education Committee of China
Biography: Ni Mingjiu (1969-) |
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Keywords: | IRS scheme four_stage Runge_Kutta technique TVD scheme |
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