Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems
Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems
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点隐式龙格-库塔方法在无粘流问题中的研究和应用
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发表时间：
2012
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通讯作者：
S. Langer
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作者：
S. Langer
我们推导并研究了点隐式Runge-Kutta方法，以显著提高收敛速度以逼近无粘流的定常解。结果表明，点隐式Runge-Kutta方法可以被解释为一种预条件显式Runge-Kutta方法，其中预条件算子自然地作为残差函数的局部导数产生。此外，到目前为止文献中提出的许多预条件式都被认为是我们一般情况下的特例。条件将被表述为具有局部时间步长的显式Runge-Kutta方法与点隐式方法等价。在数值例子中，我们将证明改进的收敛速度。版权所有©2011 John Wiley&Sons，Ltd.
We derive and investigate point implicit Runge–Kutta methods to significantly improve the convergence rate to approximate steady‐state solutions of inviscid flows. It turns out that the point implicit Runge–Kutta can be interpreted as a preconditioned explicit Runge–Kutta method, where the preconditioner arises naturally as local derivative of the residual function. Moreover, many preconditioners suggested in the literature so far are identified as special case of our general ansatz. Conditions will be formulated such that explicit Runge–Kutta methods with local time stepping are equivalent to point implicit methods. In numerical examples, we will demonstrate the improved convergence rates. Copyright © 2011 John Wiley & Sons, Ltd.