Efficient Implicit Time-Marching Methods Using a Newton-Krylov Algorithm
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Bibliographic record
Abstract
The numerical behavior of two implicit time-marching methods is investigated in solving two-dimensional unsteady compressible flows. The two methods are the second-order multistep backward differencing formula and the fourth-order multistage explicit first stage, single-diagonal coefficient, diagonally implicit Runge-Kutta scheme. A Newton-Krylov method is used to solve the nonlinear problem arising from the implicit temporal discretization. The methods are studied for two test cases: laminar flow over a cylinder and turbulent flow over a NACA0012 airfoil with a blunt trailing edge. Parameter studies show that the subiteration termination criterion plays a major role in the efficiency of time-marching methods. Efficiency studies show that when only modest global accuracy is needed, the second-order method is preferred. The fourth-order method is more efficient when high accuracy is required. The Newton-Krylov method is seen to be an efficient choice for implicit time-accurate computations.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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