Quinpi: Integrating Conservation Laws with CWENO Implicit Methods
| Autor: | G. Puppo, M. Semplice, G. Visconti |
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| Rok vydání: | 2022 |
| Předmět: |
Computational Mathematics
Essentially non-oscillatory schemes Finite volumes Implicit schemes WENO and CWENO reconstructions Applied Mathematics FOS: Mathematics Computer Science::Mathematical Software Numerical Analysis (math.NA) Mathematics - Numerical Analysis 65M08 65M20 35L65 65L04 Computer Science::Digital Libraries |
| Zdroj: | Communications on Applied Mathematics and Computation. 5:343-369 |
| ISSN: | 2661-8893 2096-6385 |
| DOI: | 10.1007/s42967-021-00171-0 |
| Popis: | Many interesting applications of hyperbolic systems of equations are stiff, and require the time step to satisfy restrictive stability conditions. One way to avoid small time steps is to use implicit time integration. Implicit integration is quite straightforward for first-order schemes. High order schemes instead also need to control spurious oscillations, which requires limiting in space and time also in the linear case. We propose a framework to simplify considerably the application of high order non-oscillatory schemes through the introduction of a low order implicit predictor, which is used both to set up the nonlinear weights of a standard high order space reconstruction, and to achieve limiting in time. In this preliminary work, we concentrate on the case of a third-order scheme, based on diagonally implicit Runge Kutta ($$\mathsf {DIRK}$$ DIRK ) integration in time and central weighted essentially non-oscillatory ($$\mathsf {CWENO}$$ CWENO ) reconstruction in space. The numerical tests involve linear and nonlinear scalar conservation laws. |
| Databáze: | OpenAIRE |
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