Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws

Shijian Lin, Qi Luo, Hongze Leng and Junqiang Song
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Shijian Lin: College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China
Qi Luo: Department of Mathematics, National University of Defense Technology, Changsha 410000, China
Hongze Leng: College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China
Junqiang Song: College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China

Mathematics, 2021, vol. 9, issue 16, 1-24

Abstract: 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.

Keywords: hyperbolic conservation laws; multi-moment; high-order accuracy; local reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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