Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Splitting Method for Time-dependent Convection-dominated Diffusion
  Problems   We present a new splitting method for time-dependent convection-dominated
diffusion problems. The original convection diffusion system is split into two
sub-systems: a pure convection system and a diffusion system. At each time
step, a convection problem and a diffusion problem are solved successively. The
scheme has the following nice features: the convection subproblem is solved
explicitly and a multistep technique is introduced to essentially enlarge the
stability region so that the resulting scheme behaves like an unconditionally
stable scheme; the diffusion subproblem is always self-adjoint and coercive so
that it can be solved efficiently using many existing optimal preconditioned
iterative solvers. The scheme is then extended for Navier-Stokes equations,
where the nonlinear convection is resolved by a linear explicit multistep
scheme at the convection step, and only a generalized Stokes problem is needed
to solve at the diffusion step with the resulting stiffness matrix being
invariant in the time marching process. The new schemes are all free from
tuning some stabilization parameters for the convection-dominated diffusion
problems. Numerical simulations are presented to demonstrate the stability,
convergence and performance of the single-step and multistep variants of the
new scheme.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an