Abstract
A localized radial basis function (RBF) meshless method is developed for coupled viscous
fluid flow and convective heat transfer problems. The method is based on new localized
radial-basis function (RBF) expansions using Hardy Multiquadrics for the sought-after
unknowns. An efficient set of formulae are derived to compute the RBF interpolation in
terms of vector products thus providing a substantial computational savings over traditional meshless methods. Moreover, the approach developed in this paper is applicable to
explicit or implicit time marching schemes as well as steady-state iterative methods. We
apply the method to viscous fluid flow and conjugate heat transfer (CHT) modeling. The
incompressible Navier–Stokes are time marched using a Helmholtz potential decomposition for the velocity field. When CHT is considered, the same RBF expansion is used to
solve the heat conduction problem in the solid regions enforcing temperature and heat
flux continuity of the solid/fluid interfaces. The computation is accelerated by distributing
the load over several processors via a domain decomposition along with an interface
interpolation tailored to pass information through each of the domain interfaces to ensure
conservation of field variables and derivatives. Numerical results are presented for several cases including channel flow, flow in a channel with a square step obstruction, and
a jet flow into a square cavity. Results are compared with commercial computational fluid
dynamics code predictions. The proposed localized meshless method approach is shown
to produce accurate results while requiring a much-reduced effort in problem preparation
in comparison to other traditional numerical methods
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