TY - JOUR
T1 - A High Order Semi-Lagrangian Discontinuous Galerkin Method for the Two-Dimensional Incompressible Euler Equations and the Guiding Center Vlasov Model Without Operator Splitting
AU - Cai, Xiaofeng
AU - Guo, Wei
AU - Qiu, Jing Mei
N1 - Funding Information:
W. Guo: Research is supported by NSF Grant NSF-DMS-1620047. J.-M. Qiu: Research of first and last author is supported by NSF Grant NSF-DMS-1522777 and 1818924, Air Force Office of Scientific Computing FA9550-18-1-0257 and University of Delaware.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/5/15
Y1 - 2019/5/15
N2 - In this paper, we generalize a high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for multi-dimensional linear transport equations without operator splitting developed in Cai et al. (J Sci Comput 73(2–3):514–542, 2017) to the 2D time dependent incompressible Euler equations in the vorticity-stream function formulation and the guiding center Vlasov model. We adopt a local DG method for Poisson’s equation of these models. For tracing the characteristics, we adopt a high order characteristics tracing mechanism based on a prediction-correction technique. The SLDG with large time-stepping size might be subject to extreme distortion of upstream cells. To avoid this problem, we propose a novel adaptive time-stepping strategy by controlling the relative deviation of areas of upstream cells.
AB - In this paper, we generalize a high order semi-Lagrangian (SL) discontinuous Galerkin (DG) method for multi-dimensional linear transport equations without operator splitting developed in Cai et al. (J Sci Comput 73(2–3):514–542, 2017) to the 2D time dependent incompressible Euler equations in the vorticity-stream function formulation and the guiding center Vlasov model. We adopt a local DG method for Poisson’s equation of these models. For tracing the characteristics, we adopt a high order characteristics tracing mechanism based on a prediction-correction technique. The SLDG with large time-stepping size might be subject to extreme distortion of upstream cells. To avoid this problem, we propose a novel adaptive time-stepping strategy by controlling the relative deviation of areas of upstream cells.
KW - Adaptive time-stepping method
KW - Discontinuous Galerkin
KW - Guiding center Vlasov model
KW - Incompressible Euler equations
KW - Mass conservative
KW - Non-splitting
KW - Semi-Lagrangian
UR - http://www.scopus.com/inward/record.url?scp=85064554995&partnerID=8YFLogxK
U2 - 10.1007/s10915-018-0889-1
DO - 10.1007/s10915-018-0889-1
M3 - Article
AN - SCOPUS:85064554995
SN - 0885-7474
VL - 79
SP - 1111
EP - 1134
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
ER -