7 papers
Numerical analysis of a bdf2 modular grad-div Stabilization method for the Navier-Stokes equations
Y. Rong, J. A. Fiordilino
A second-order accurate modular algorithm is presented for a standard BDF2 code for the Navier-Stokes equations (NSE). The algorithm exhibits resistance to solver breakdown and inc…
An Artificial Compressibility Ensemble Timestepping Algorithm for Flow Problems
Joseph A. Fiordilino, Michael McLaughlin
Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To rea…
Robust and Efficient Modular Grad-Div Stabilization
Joseph Anthony Fiordilino, William Layton, Yao Rong
This paper presents two modular grad-div algorithms for calculating solutions to the Navier-Stokes equations (NSE). These algorithms add to an NSE code a minimally intrusive module…
A Discrete Hopf Interpolant and Stability of the Finite Element Method for Natural Convection
Joseph A. Fiordilino, Ali Pakzad
The temperature in natural convection problems is, under mild data assumptions, uniformly bounded in time. This property has not yet been proven for the standard finite element met…
Ensemble Timestepping Algorithms for the Heat Equation with Uncertain Conductivity
Joseph A. Fiordilino
Motivated by applications to 3D printing, this paper presents two algorithms for calculating an ensemble of solutions to heat conduction problems. The ensemble average is the most…
A Second Order Ensemble Timestepping Algorithm for Natural Convection
Joseph A. Fiordilino
This paper presents an algorithm for calculating an ensemble of solutions to natural convection problems. The ensemble average is the most likely temperature distribution and its v…