arXiv subjects

Zhihui Zou

Publications and source records attributed to Zhihui Zou.

7 recordsLinked to original sources

arXiv2025

A simple and efficient hybrid discretization approach to alleviate membrane locking in isogeometric thin shells

This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation. It does not increase the bandwidth of the tangent matrix and is effective for both linear and nonlinear problems. It combines isogeometric surface discretizations with classical Lagrange-based surface discretizations, and can thus be run with existing isogeometric finite element codes. Also, the stresses can be recovered straightforwardly. The effectiveness of the proposed approach in alleviating, if not eliminating, membrane locking is demonstrated through the rigorous study of the convergence behavior of several classical benchmark problems. Accuracy gains are particularly large in the membrane stresses. The approach is formulated here for quadratic NURBS, but an extension to other discretization types can be anticipated. The same applies to other constraints and associated locking phenomena.

cs.CE↗

arXiv2024

A conservative, implicit solver for 0D-2V multi-species nonlinear Fokker-Planck collision equations

In this study, we present an optimal implicit algorithm specifically designed to accurately solve the multi-species nonlinear 0D-2V axisymmetric Fokker-Planck-Rosenbluth (FPR) collision equation while preserving mass, momentum, and energy. Our approach relies on the utilization of nonlinear Shkarofsky's formula of FPR (FPRS) collision operator in the spherical-polar coordinate. The key innovation lies in the introduction of a new function named King, with the adoption of the Legendre polynomial expansion for the angular coordinate and King function expansion for the speed coordinate. The Legendre polynomial expansion will converge exponentially and the King method, a moment convergence algorithm, could ensure the conservation with high precision in discrete form. Additionally, post-step projection onto manifolds is employed to exactly enforce symmetries of the collision operators. Through solving several typical problems across various nonequilibrium configurations, we demonstrate the high accuracy and superior performance of the presented algorithm for weakly anisotropic plasmas.

math.NA↗

arXiv2022

Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the Long-Lived Mode (LLM) frequency multiplication with n = 1,2,3 or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that, when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ("frequency multiplication"), even in absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at magnetic axis q0 varies. In absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that the higher-n modes are more vulnerable to EPs. These results may shed light on the understanding about the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.

physics.plasm-ph↗

arXiv2021

Transition from fishbone mode to $β$-induced Alfvén eigenmode on HL-2A tokamak

In the presence of energetic particles (EPs) from auxiliary heating and burning plasmas, fishbone instability and Alfvén modes can be excited and their transition can take place in certain overlapping regimes. Using the hybrid kinetic-magnetohydrodynamic model in the NIMROD code, we have identified such a transition between the fishbone instability and the $β$-induced Alfvén Eigenmode (BAE) for the NBI heated plasmas on HL-2A. When the safety factor at magnetic axis is well below one, typical kink-fishbone transition occurs as the EP fraction increases. When $q_0$ is raised to approaching one, the fishbone mode is replaced with BAE for sufficient amount of EPs. When $q_0$ is slightly above one, the toroidicity-induced Alfvén eigenmode (TAE) dominates at lower EP pressure, whereas BAE dominates at higher EP pressure.

physics.plasm-ph↗

arXiv2019

Numerical study of transition between even and odd toroidal Alfvén eigenmodes on EAST

Linear simulations of toriodal Alfvén eigenmodes (TAEs) driven by energetic particles (EPs) on EAST (Experimental Advanced Superconducting Tokamak) are performed using the hybrid-kinetic MHD (HK-MHD) model implemented in NIMROD code. The EAST equilibrium is reconstructed using the EFIT code based on experimental measurement. The "slowing down" distribution is adopted for modeling the equilibrium distribution of the energetic ions from the deuterium neutral beam injection on EAST. The frequency, the dominant poloidal mode number, the radial location and the detailed 2D mode structure of the TAE/RSAE/EPM modes are consistent between the eigenvalue analysis and the NIMROD simulation. As the $β$ fraction of EP increases, a transition between even and odd TAEs occurs, along with that between the ballooning and anti-ballooning mode structures. When the $β$ fraction of EP is close to the transition threshold, both types of TAEs coexist.

physics.plasm-ph↗

arXiv2019

Isogeometric Bézier dual mortaring: The biharmonic problem

In this paper we develop an isogeometric Bézier dual mortar method for the biharmonic problem on multi-patch domains. The well-posedness of the discrete biharmonic problem requires a discretization with $C^1$ continuous basis functions. Hence, two Lagrange multipliers are required to apply both $C^0$ and $C^1$ continuity constraints on each intersection. The dual mortar method utilizes dual basis functions to discretize the Lagrange multiplier spaces. In order to preserve the sparsity of the coupled problem, we develop a dual mortar suitable $C^1$ constraint and utilize the Bézier dual basis to discretize the Lagrange multiplier spaces. The Bézier dual basis functions are constructed through Bézier projection and possess the same support size as the corresponding B-spline basis functions. We prove that this approach leads to a well-posed discrete problem and specify requirements to achieve optimal convergence. Although the Bézier dual basis is sub-optimal due to the lack of polynomial reproduction, our formulation successfully postpones the domination of the consistency error for practical problems. We verify the theoretical results and demonstrate the performance of the proposed formulation through several benchmark problems.

math.NA↗

arXiv2017

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity (ITPA) group, is studied in this work. Numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a delta f particle-in-cell (PIC) representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from eigen-analysis calculations and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. When the density and temperature of EP distribution are above certain threshold, the transition from TAE to EPM occurs and the mode structure changes.

physics.plasm-ph↗