56 citations · 62 across the 9 of their papers we have counts for
11 papers
Data Assimilation with Sparse Observations
Nan Jiang, William Layton, Nanda Nechingal Raghunathan +1
Data assimilation by nudging (also called CDA) yields exponentially decaying errors and an infinite predictability horizon if the method parameter is large enough and the observati…
A family of second order, linear, unconditionally stable methods for the Cahn-Hilliard-Navier-Stokes equations
Daozhi Han, Nan Jiang, Jonah H. Nissan +1
We present a family of second-order, linear, unconditionally stable implicit-explicit (IMEX) methods for the Cahn-Hilliard-Navier-Stokes (CHNS) equations modeling matched-density t…
Second order, unconditionally stable, linear ensemble algorithms for the magnetohydrodynamics equations
John Carter, Daozhi Han, Nan Jiang
We propose two unconditionally stable, linear ensemble algorithms with pre-computable shared coefficient matrices across different realizations for the magnetohydrodynamics equatio…
Three linear, unconditionally stable, second order decoupling methods for the Allen--Cahn--Navier--Stokes phase field model
Ruonan Cao, Nan Jiang, Huanhuan Yang
Hydrodynamics coupled phase field models have intricate difficulties to solve numerically as they feature high nonlinearity and great complexity in coupling. In this paper, we prop…
A second-order Ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations
Nan Jiang
We present a second-order ensemble method based on a blended three-step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier-Stokes equations…
A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations
Max Gunzburger, Nan Jiang, Michael Schneier
Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as oc…
A second-order time-stepping scheme for simulating ensembles of parameterized flow problems
Max Gunzburger, Nan Jiang, Zhu Wang
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or…
An efficient algorithm for simulating ensembles of parameterized flow problems
Max Gunzburger, Nan Jiang, Zhu Wang
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to effi…
Analysis and approximation of a fractional Laplacian-based closure model for turbulent flows and its connection to Richardson pair dispersion
Max Gunzburger, Nan Jiang, Feifei Xu
We study a turbulence closure model in which the fractional Laplacian of the velocity field represents the turbulence diffusivity. We investigate the energy spectrum of th…
An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations
Max Gunzburger, Nan Jiang, Michael Schneier
The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of para…
Algorithms and Models for Turbulence Not at Statistical Equilibrium
Nan Jiang, William Layton
Standard eddy viscosity models, while robust, cannot represent backscatter and have severe difficulties with complex turbulence not at statistical equilibrium. This report gives a…