Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws

Mathematics

Hongze Leng¹  Junqiang Song¹  Shijian Lin¹  Qi Luo² 

[1] College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410000, China;Department of Mathematics, National University of Defense Technology, Changsha 410000, China;

关键词: hyperbolic conservation laws;    multi-moment;    high-order accuracy;    local reconstruction;   

DOI  :  10.3390/math9161885

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown