This paper presents the limited reconstruction of high-order spectral volume (SV) methods that rigorously satisfy the maximum principle and preserve positivity for scalar hyperbolic conservation laws and the compressible Euler equations, respectively. Standard high-order numerical methods often violate these physical constraints at the discrete level, leading to nonphysical oscillations and solutions—such as negative density or pressure. To address this, we introduce carefully designed limiter functions that modify the SV reconstruction polynomials within each cell while maintaining the scheme’s high-order accuracy. This approach enforces the maximum-principle-preserving (MPP) and positivity-preserving (PP) properties in the numerical solution. A set of numerical tests shows that the method produces accurate, stable results for both smooth and discontinuous problems, confirming its high resolution and robustness.
Farzi, J. (2026). High-Accuracy Spectral Volume Reconstructions with Maximum-Principle-Satisfying and Positivity-Preserving Properties for Hyperbolic Problems. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.69117.3397
MLA
Farzi, J. . "High-Accuracy Spectral Volume Reconstructions with Maximum-Principle-Satisfying and Positivity-Preserving Properties for Hyperbolic Problems", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.69117.3397
HARVARD
Farzi, J. (2026). 'High-Accuracy Spectral Volume Reconstructions with Maximum-Principle-Satisfying and Positivity-Preserving Properties for Hyperbolic Problems', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.69117.3397
CHICAGO
J. Farzi, "High-Accuracy Spectral Volume Reconstructions with Maximum-Principle-Satisfying and Positivity-Preserving Properties for Hyperbolic Problems," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.69117.3397
VANCOUVER
Farzi, J. High-Accuracy Spectral Volume Reconstructions with Maximum-Principle-Satisfying and Positivity-Preserving Properties for Hyperbolic Problems. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.69117.3397
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