Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations. (English) Zbl 0986.76060
From the summary: We derive low-storage, explicit Runge-Kutta (ERK) schemes in the context of integrating compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Sixteen ERK pairs are presented using from two to five registers of memory per equation and per grid point, and having accuracies from third- to fifth-order. Methods have been tested with the one-dimensional wave equation.
MSC:
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76N15 | Gas dynamics (general theory) |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
Keywords:
low-storage explicit Runge-Kutta schemes; compressible Navier-Stokes equations; direct numerical simulation; stability; accuracy; error control; step change; one-dimensional wave equationReferences:
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