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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
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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