11,765 research outputs found
Consistent forcing scheme in the cascaded lattice Boltzmann method
In this paper, we give a more pellucid derivation for the cascaded lattice
Boltzmann method (CLBM) based on a general multiple-relaxation-time (MRT) frame
through defining a shift matrix. When the shift matrix is a unit matrix, the
CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is
developed for the CLBM. The applicability of the non-slip rule, the
second-order convergence rate in space and the property of isotropy for the
consistent forcing scheme is demonstrated through the simulation of several
canonical problems. Several other existing force schemes previously used in the
CLBM are also examined. The study clarifies the relation between MRT LBM and
CLBM under a general framework
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
While nonlinear stochastic partial differential equations arise naturally in
spatiotemporal modeling, inference for such systems often faces two major
challenges: sparse noisy data and ill-posedness of the inverse problem of
parameter estimation. To overcome the challenges, we introduce a strongly
regularized posterior by normalizing the likelihood and by imposing physical
constraints through priors of the parameters and states. We investigate joint
parameter-state estimation by the regularized posterior in a physically
motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate
reconstruction. The high-dimensional posterior is sampled by a particle Gibbs
sampler that combines MCMC with an optimal particle filter exploiting the
structure of the SEBM. In tests using either Gaussian or uniform priors based
on the physical range of parameters, the regularized posteriors overcome the
ill-posedness and lead to samples within physical ranges, quantifying the
uncertainty in estimation. Due to the ill-posedness and the regularization, the
posterior of parameters presents a relatively large uncertainty, and
consequently, the maximum of the posterior, which is the minimizer in a
variational approach, can have a large variation. In contrast, the posterior of
states generally concentrates near the truth, substantially filtering out
observation noise and reducing uncertainty in the unconstrained SEBM
- …