Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the construction of conservative semi-Lagrangian IMEX advection
  schemes for multiscale time dependent PDEs   This article is devoted to the construction of a new class of semi-Lagrangian
(SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for
PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach
fully couples the space and time discretization, thus making the use of RK
strategies particularly difficult to be combined with. First, a simple scalar
advection-diffusion equation is considered as a prototype PDE for the
development of a high order formulation of the semi-Lagrangian IMEX algorithms.
The advection part of the PDE is discretized explicitly at the aid of a SL
technique, while an implicit discretization is employed for the diffusion
terms. Second, the SL-IMEX approach is extended to deal with hyperbolic systems
with multiple scales, including balance laws, that involve shock waves and
other discontinuities. A novel SL technique is proposed, which is based on the
integration of the governing equations over the space-time control volume which
arises from the motion of each grid point. High order of accuracy is ensured by
the usage of IMEX RK schemes combined with a Cauchy-Kowalevskaya procedure that
provides a predictor solution within each space-time element. The
one-dimensional shallow water equations (SWE) are chosen to validate the new
conservative SL-IMEX schemes, where convection and pressure fluxes are treated
explicitly and implicitly, respectively. The asymptotic-preserving (AP)
property of the novel schemes is also studied considering a relaxation PDE
system for the SWE. A large suite of convergence studies for both the
non-conservative and the conservative version of the novel class of methods
demonstrates that the formal order of accuracy is achieved and numerical
evidences about the conservation property are shown. The AP property for the
corresponding relaxation system is also investigated.

14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio