Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy-based operator splitting approach for the time discretization of
  coupled systems of partial and ordinary differential equations for fluid
  flows: The Stokes case   The goal of this work is to develop a novel splitting approach for the
numerical solution of multiscale problems involving the coupling between Stokes
equations and ODE systems, as often encountered in blood flow modeling
applications. The proposed algorithm is based on a semi-discretization in time
based on operator splitting, whose design is guided by the rationale of
ensuring that the physical energy balance is maintained at the discrete level.
As a result, unconditional stability with respect to the time step choice is
ensured by the implicit treatment of interface conditions within the Stokes
substeps, whereas the coupling between Stokes and ODE substeps is enforced via
appropriate initial conditions for each substep. Notably, unconditional
stability is attained without the need of subiterating between Stokes and ODE
substeps. Stability and convergence properties of the proposed algorithm are
tested on three specific examples for which analytical solutions are derived.

25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg