Linear finite-difference methods of higher than first-order accuracy applied to the calculation of 1-D unsteady flow inevitably produce numerical overshoot at discontinuities. Several remedies have been proposed in the past; a simple and effective one is flux correction. We propose it in the naive form, which destroys neither the order of accuracy nor the stability of the underlying method. Particular problems arise at the boundaries, where appropriate precautions help to fulfill the conservation laws. Additionally allowing for elasticity of the valve control system, results with acceptable accuracy are obtained in supercharging practice. A comparison of computing time, accuracy and storage requirements confirms the advantages of naive flux correction.

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