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 schemes, our approach updates model variables implementing two reconstructions alternately. First, Hermite interpolation reconstructs solution within cell matching point-based containing both physical values and their spatial derivatives. Then reconstructed is updated Euler method. Second, we solve constrained least-squares problem to correct preserve laws. Our method enjoys advantages of compact stencil high-order accuracy. Fourier analysis also indicates that allows larger CFL number compared with many other schemes. By adding proper amount artificial viscosity, shock waves discontinuities can be computed accurately sharply without solving an approximated Riemann problem.