Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws

We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing multi-moment schemes, our approach updates model variables by implementing two polynomial reconstructions alternately. First, Hermite interpola...

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Veröffentlicht in:Mathematics (Basel) 2021-08, Vol.9 (16), p.1885
Hauptverfasser: Lin, Shijian, Luo, Qi, Leng, Hongze, Song, Junqiang
Format: Artikel
Sprache:eng
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Zusammenfassung:We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing multi-moment schemes, our approach updates model variables by implementing two polynomial reconstructions alternately. First, Hermite interpolation reconstructs the solution within the cell by matching the point-based variables containing both physical values and their spatial derivatives. Then the reconstructed solution is updated by the Euler method. Second, we solve a constrained least-squares problem to correct the updated solution to preserve the conservation laws. Our method enjoys the advantages of a compact numerical stencil and high-order accuracy. Fourier analysis also indicates that our method allows a larger CFL number compared with many other high-order schemes. By adding a proper amount of artificial viscosity, shock waves and other discontinuities can also be computed accurately and sharply without solving an approximated Riemann problem.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9161885