Positivity-preserving WENO schemes with constrained transport for ideal magnetohydrodynamic equations

机译：理想磁磁流体方程的带约束输运的保正WENO方案

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Summary form only given. A novel positivity-preserving flux limiting technique is developed for finite difference WENO schemes to solve the idea magnetohydrodynamic (MHD) equations. The key challenges in applying such methods to ideal MHD are not only maintaining the positivity of density and pressure but also controlling divergence errors in the magnetic field. These two requirements are fulfilled by two steps: first implementing positivity-preserving flux limiter on the base WENO solver and then correcting the magnetic field and the total energy by a high-order constrained transport approach that is based on evolving the magnetic potential. Several 1D, 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to demonstrate the importance and efficiency to maintain the positivity of the solution of test problems including low-beta plasma flows.

机译：仅提供摘要表格。针对有限差分WENO方案，开发了一种新颖的保正通量限制技术，以解决磁流体动力学（MHD）方程的问题。将此类方法应用于理想MHD的关键挑战不仅在于保持密度和压力的正值，还在于控制磁场中的发散误差。这两个要求可以通过两个步骤来满足：首先在基本的WENO求解器上实现保正磁通量限制器，然后通过基于演化磁势的高阶约束传输方法来校正磁场和总能量。给出了几个1D，2D和3D数值示例，以验证在平滑测试问题上的准确性顺序，并证明保持包括低β等离子体流在内的测试问题解决方案的积极性的重要性和效率。

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《The 41st IEEE International Conference on Plasma Science, and the 20th International Conference on High-Power Particle Beams》|2014年|1-1|共1页
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Qi Tang; Yuan Liu; Christlieb Andrew; Zhengfu Xu;
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finite difference methods; plasma magnetohydrodynamics; plasma transport processes; MHD; density positivity; divergence errors; finite difference WENO schemes; high-order constrained transport approach; ideal magnetohydrodynamic equations; low-beta plasma flows; magnetic field; magnetic potential; positivity-preserving WENO schemes; positivity-preserving flux limiting technique; pressure positivity; total energy; Computers; Educational institutions; Equations; Limiting; Magnetic fields; Magnetohydrodynamics;

机译：有限差分法;等离子体磁流体动力学;等离子体输运过程; MHD;密度正性;发散误差;有限差分WENO方案;高阶约束输运方法;理想的磁流体动力学方程式;低β等离子体流;磁场;磁势;保持正性WENO方案;保正通量限制技术;正压;总能量;计算机;教育机构;方程;极限;磁场;磁流体动力学;

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专利

1. POSITIVITY-PRESERVING FINITE DIFFERENCE WEIGHTED ENO SCHEMES WITH CONSTRAINED TRANSPORT FOR IDEAL MAGNETOHYDRODYNAMIC EQUATIONS [J] . Christlieb Andrew J., Liu Yuan, Tang Qi, SIAM Journal on Scientific Computing . 2015,第4期

机译：理想磁氢动力方程组的约束传输的保正性有限差分加权ENO格式
2. E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO Scheme [J] . Shen Y., Zha G., Huerta M.A. Journal of Computational Physics . 2012,第19期

机译：高阶WENO方案的理想磁流体动力学方程的E-CUSP方案
3. Positivity-Preserving Finite Difference WENO Scheme for Ten-Moment Equations with Source Term [J] . Meena Asha Kumari, Kumar Rakesh, Chandrashekar Praveen Journal of Scientific Computing . 2020,第1期

机译：含源项的十阶方程的保正有限差分WENO格式
4. Positivity-preserving WENO schemes with constrained transport for ideal magnetohydrodynamic equations [C] . Qi Tang, Yuan Liu, Christlieb Andrew, IEEE International Conference on Plasma Science;International Conference on High-Power Particle Beams . 2014

机译：具有理想磁流体动力学方程的受约束传输的阳性保留Weno方案
5. High order finite difference WENO schemes for ideal magnetohydrodynamics. [D] . Feng, Xiao. 2017

机译：理想磁流体动力学的高阶有限差分WENO方案。
6. An Unconditionally Stable Positivity-Preserving Splitting Scheme for Nonlinear Black-Scholes Equation with Transaction Costs [O] . Jianqiang Guo, Wansheng Wang -1

机译：具有交易成本的非线性Black-Scholes方程的无条件稳定保正分裂方案
7. Positivity-Preserving Finite Difference WENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations [O] . Christlieb, Andrew J., Liu, Yuan, Tang, Qi, 2015

机译：具有约束条件的积极保持有限差分WENO格式理想磁流体动力学方程的传输
8. Positivity-preserving High Order Finite Difference WENO Schemes for Compressible Euler Equations [R] . Zhang, X., Shu, C. 2011

机译：可压缩Euler方程的保持性高阶有限差分WENO格式

Positivity-preserving WENO schemes with constrained transport for ideal magnetohydrodynamic equations

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