TY - JOUR
T1 - Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations
AU - Yuan , Weixiong
AU - Liu , Tiegang
AU - Zhang , Bin
AU - Cao , Kui
AU - Wang , Kun
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 1
EP - 36
PY - 2024
DA - 2024/02
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0088
UR - https://global-sci.org/intro/article_detail/nmtma/22909.html
KW - Direct discontinuous Galerkin, central difference schemes, multidomain hybrid methods, viscous terms, hyperbolic-parabolic equations.
AB - <p style="text-align: justify;">A class of multidomain hybrid methods of direct discontinuous Galerkin
(DDG) methods and central difference (CD) schemes for the viscous terms is proposed in this paper. Both conservative and nonconservative coupling modes are discussed. To treat the shock wave, the nonconservative coupling mode automatically
switch to conservative coupling mode to preserve the conservative property when
discontinuities pass through the artificial interface. To maintain the accuracy of the
hybrid methods, the Lagrange interpolation polynomials and their derivatives are
reconstructed to handle the coupling cells in the DDG subdomain, while the values
of ghost points for the CD subdomain are calculated by the approximate polynomials
from the DDG methods. The linear stabilities of these methods are demonstrated in
detail through von-Neumann analysis. The multidomain hybrid DDG and CD methods are then extended to one- and two-dimensional hyperbolic-parabolic equations.
Numerical results validate that the multidomain hybrid methods are high-order accurate in the smooth regions, robust for viscous shock simulations and capable to
save computational cost.</p>