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Full-Text Articles in Physical Sciences and Mathematics
Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang
Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang
Mathematics and Statistics Faculty Research & Creative Works
We Propose Two Unconditionally Stable, Linear Ensemble Algorithms with Pre-Computable Shared Coefficient Matrices Across Different Realizations for the Magnetohydrodynamics Equations. the Viscous Terms Are Treated by a Standard Perturbative Discretization. the Nonlinear Terms Are Discretized Fully Explicitly within the Framework of the Generalized Positive Auxiliary Variable Approach (GPAV). Artificial Viscosity Stabilization that Modifies the Kinetic Energy is Introduced to Improve Accuracy of the GPAV Ensemble Methods. Numerical Results Are Presented to Demonstrate the Accuracy and Robustness of the Ensemble Algorithms.
Efficient High Order Ensemble For Fluid Flow, John Carter
Efficient High Order Ensemble For Fluid Flow, John Carter
Doctoral Dissertations
"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate …
Numerical Analysis Of A Second Order Ensemble Method For Evolutionary Magnetohydrodynamics Equations At Small Magnetic Reynolds Number, John Carter, Nan Jiang
Numerical Analysis Of A Second Order Ensemble Method For Evolutionary Magnetohydrodynamics Equations At Small Magnetic Reynolds Number, John Carter, Nan Jiang
Mathematics and Statistics Faculty Research & Creative Works
We study a second order ensemble method for fast computation of an ensemble of magnetohydrodynamics flows at small magnetic Reynolds number. Computing an ensemble of flow equations with different input parameters is a common procedure for uncertainty quantification in many engineering applications, for which the computational cost can be prohibitively expensive for nonlinear complex systems. We propose an ensemble algorithm that requires only solving one linear system with multiple right-hands instead of solving multiple different linear systems, which significantly reduces the computational cost and simulation time. Comprehensive stability and error analyses are presented proving conditional stability and second order in …