fanzhan

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Academic Interests

My primary academic interest is to develop numerical techniques for modeling multi-scale fluid & plasma dynamics that are typically described by nonlinear hyperbolic partial differential equations. In particular, I have mainly contributed to the development of shock-capturing numerical methods and solar atmospheric modeling. I am now striving to improve the modeling of the solar atmosphere, by (1) further exploring fundamental dynamics in the lower solar atmosphere, and (2) using advanced numerical techniques such as model order reduction and uncertainty quantification.

Background

I obtained my Ph.D. degree in computational mechanics from the Dalian University of Technology, where I worked at an interdisciplinary group across the Department of Engineering Mechanics and School of Aeronautics and Astronautics. Then, I continued postdoctoral research at Sun Yat-sen University and KU Leuven successively, while having extended my academic interests to MHD modeling and solar physics.

Employment

08/2023-present Postdoctoral Fellow, at Rosseland Centre for Solar Physics, Institute of Theoretical Astrophysics, University of Oslo.
08/2019-07/2023 Postdoctoral Fellow, at Centre for mathematical Plasma-Astrophysics, Department of Mathematics, KU Leuven.
03/2018-01/2020 Postdoctoral Researcher, at School of Aeronautics and Astronautics, Sun Yat-sen University.

Zhang, Fan; Lani, Andrea & Poedts, Stefaan (2026). On energy consistency of intermediate states in HLL-type MHD Riemann solvers. Journal of Computational Physics. ISSN 0021-9991. 553. doi: 10.1016/j.jcp.2026.114724. Full text in Research Archive Show summary
Approximate Riemann solvers are widely used for solving hyperbolic conservation laws, including those of magnetohydrodynamics (MHD). However, due to the nonlinearity and complexity of MHD, obtaining accurate and robust numerical solutions to MHD equations is non-trivial, and it may be challenging for an approximate MHD Riemann solver to preserve the positivity of scalar variables, particularly when the plasma β is low. As we have identified that the inconsistency between the numerically calculated magnetic field and magnetic energy may be at least partly responsible for the loss of positivity of scalar variables, we propose a consistency condition for calculating the intermediate energies within the Riemann fan and implement it in HLL-type MHD Riemann solvers, thereby alleviating erroneous magnetic field solutions that break scalar positivity. In addition, (I) for the HLLC-type scheme, we have designed a revised two-state approximation, specifically reducing numerical error in magnetic field solutions, although sacrificing the contact-resolving capability, and (II) for the HLLD-type scheme, we replace the constant total pressure assumption by a three-state assumption for the intermediate thermal energy, which is more consistent with our other assumptions. The proposed schemes perform better in numerical examples with low plasma β. Moreover, we explained the energy error introduced during time integration.
Wang, H. P.; Poedts, S.; Lani, A.; Linan, L.; Baratashvili, T. & Zhang, F. [Show all 11 contributors for this article] (2025). Time-evolving coronal modelling of the solar maximum around the solar storms in May 2024 by COCONUT. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 702. doi: 10.1051/0004-6361/202555760. Full text in Research Archive Show summary
Context. Time-evolving magnetohydrodynamic (MHD) coronal models driven by a sequence of time-evolving photospheric magnetograms deliver more realistic results than traditional quasi-steady-state models constrained by a static magnetogram. The fully implicit time-evolving coronal model COCONUT performs efficiently enough for real-time coronal simulations during solar minimum. Significant challenges persist in modelling the more complex coronal evolutions of solar maximum scenarios, however. Aims. During solar maxima, the coronal magnetic field is more complex and stronger, and coronal structures evolve more rapidly than during solar minima. Consequently, time-evolving MHD coronal modelling of solar maxima often struggles with poor numerical stability and low computational efficiency. We enhanced the numerical stability of the time-evolving coronal model COCONUT to mitigate these issues with the aim to evaluate the differences between the time-evolving and quasi-steady-state coronal simulation results, and to assess the impact of the spatial resolution on global MHD coronal modelling of solar maxima. Methods. After enhancing the positivity-preserving property of the time-evolving coronal model COCONUT, we employed it to simulate the evolution of coronal structures from the solar surface to 0.1 AU in an inertial coordinate system over two Carrington rotations around the solar storms in May 2024. These simulations were performed on unstructured geodesic meshes containing 6.06, 1.52, and 0.38 million (M) cells to assess the impact of grid resolution. We also conducted a quasi-steady-state coronal simulation that treated the solar surface as a rigidly rotating spherical shell to demonstrate the impact of the emergence and cancellation of the magnetic flux in global coronal simulations. A comparison with observations further validated the reliability of the efficient time-evolving coronal modelling technique. Results. We demonstrate that incorporating the evolution of the magnetic field in the inner boundary conditions can significantly improve the fidelity of global MHD coronal simulations around a solar maximum. A simulated magnetic field strength using a refined mesh with 6.06 M cells can be stronger by more than 40% than that in a coarser mesh with 0.38 M cells. A time step of 5 minutes and a mesh containing 1.5 M cells can effectively capture the evolution of large-scale coronal structures and small-sized dipoles. Thus, the fully implicit time-evolving model COCONUT shows promise for accurately conducting real-time global coronal simulations of solar maxima. This makes it suitable for practical applications such as daily space-weather forecasting.
Wang, H.P.; Guo, J.H.; Yang, L.P.; Poedts, S.; Zhang, Fan & Lani, A. [Show all 10 contributors for this article] (2025). SIP-IFVM: Efficient time-accurate magnetohydrodynamic model of the corona and coronal mass ejections. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 693. doi: 10.1051/0004-6361/202450771. Full text in Research Archive Show summary
Context. Coronal mass ejections (CMEs) are one of the main drivers of space weather. However, robust and efficient numerical modelling applications of the initial stages of CME propagation and evolution process in the sub-Alfvénic corona are still lacking. Aims. Magnetohydrodynamic (MHD) solar coronal models are critical in the Sun-to-Earth model chain, but they do sometimes encounter low-β (<10−4) problems near the solar surface. This paper aims to deal with these low-β problems and make MHD modelling suitable for practical space weather forecasting by developing an efficient and time-accurate MHD model of the solar corona and CMEs. In this paper, we present an efficient and time-accurate three-dimensional (3D) single-fluid MHD solar coronal model and employ it to simulate CME evolution and propagation. Methods. Based on a quasi-steady-state implicit MHD coronal model, we developed an efficient time-accurate coronal model that can be used to speed up the CME simulation by selecting a large time-step size. We have called it the Solar Interplanetary Phenomena-Implicit Finite Volume Method (SIP-IFVM) coronal model. A pseudo-time marching method was implemented to improve temporal accuracy. A regularised Biot-Savart Laws (RBSL) flux rope, whose axis can be designed into an arbitrary shape, was inserted into the background corona to trigger the CME event. We performed a CME simulation on the background corona of Carrington rotation (CR) 2219 and evaluated the impact of time-step sizes on simulation results. Our study demonstrates that this model is able to simulate the CME evolution and propagation process from the solar surface to 20 Rs in less than 0.5 hours (192 CPU cores, ~1 M cells). Compared to the explicit counterpart, this implicit coronal model is not only faster, but it also has improved numerical stability. We also conducted an ad hoc simulation with initial magnetic fields artificially increased. It shows that this model can effectively deal with time-dependent low-β problems (β < 10−4). Additionally, an Orszag-Tang MHD vortex flow simulation demonstrates that the pseudo-time-marching method used in this coronal model can simulate small-scale unsteady-state flows. Results. The simulation results show that this MHD coronal model is very efficient and numerically stable. It is a promising approach to simulating time-varying events in the solar corona with low plasma β in a timely and accurate manner.
Wang, H.P.; Poedts, S.; Lani, A.; Brchnelova, M.; Baratashvili, T. & Linan, L. [Show all 9 contributors for this article] (2025). Efficient magnetohydrodynamic modelling of the time-evolving corona by COCONUT. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 694. doi: 10.1051/0004-6361/202452279. Full text in Research Archive Show summary
Context. Magnetohydrodynamic (MHD) solar corona models are critical in the Sun-to-Earth modelling chain and are the most complex and computationally intensive component. Compared to quasi-steady-state corona models that are constrained by a time-invariant magnetogram over a Carrington rotation (CR) period, time-evolving corona models driven by time-varying photospheric magnetograms are more realistic and can maintain more useful information to accurately describe solar wind evolution and forecast coronal mass ejection propagation. Aims. Implicit methods have significantly improved the efficiency of quasi-steady MHD coronal modelling. However, developing efficient time-evolving corona models to improve space weather forecasting is also important. This paper aims to demonstrate that time-evolving corona simulations can be performed efficiently and accurately using an implicit method with relatively large time steps, thus reducing the overall computational cost. We also evaluate differences between coronal structures captured by time-evolving and quasi-steady simulations over a CR period during solar minimum. Methods. We extended the quasi-steady COCONUT model, a global MHD corona model that uses implicit methods to select large time steps, into a time-evolving corona model. Specifically, we used a series of hourly updated photospheric magnetograms to drive the evolution of coronal structures from the solar surface to 25 Rs during two CRs around the 2019 eclipse in an inertial coordinate system. At each time step, the inner-boundary magnetic field was temporal-interpolated and updated from adjacent observation-based magnetograms. We compare the time-evolving and quasi-steady simulations to demonstrate that the differences in these two types of coronal modelling can be obvious even for a solar minimum. The relative differences in radial velocity and density can be over 15% and 25% at 20 Rs during one CR period. We also evaluated the impact of time steps on the simulation results. Using a time step of approximately 10 minutes balances efficiency and necessary numerical stability and accuracy for time-evolving corona simulations around solar minima. The chosen 10-minute time step significantly exceeds the Courant-Friedrichs-Lewy stability condition needed for explicit corona modelling, and the time-evolving COCONUT can thus simulate the coronal evolution during a full CR within only 9 hours (using 1080 CPU cores for 1.5M grid cells). Results. The simulation results demonstrate that time-evolving MHD coronal simulations can be performed efficiently and accurately using an implicit method, offering a more realistic alternative to quasi-steady-state simulations. The fully implicit time-evolving corona model thus promises to simulate the time-evolving corona accurately in practical space weather forecasting.
Zhang, Fan (2024). Improving the quantification of overshooting shock-capturing oscillations. Progress in Computational Fluid Dynamics, An International Journal (CFD). ISSN 1468-4349. 24(3), p. 135–142. doi: 10.1504/PCFD.2024.138236. Full text in Research Archive Show summary
An approach for quantitatively evaluating overshooting oscillations is designed to characterise the performance of shock-capturing schemes. Specifically, following our previous work focused on cases with only discontinuities, now we account for the concurrent presences of discontinuities and smooth waves, each with a complete set of supported modes on a given discretisation. The linear advection equation is taken as the model equation, and a standardised measurement is given for overshooting oscillations produced by shock-capturing schemes. Thereby, we can quantitatively reveal the shock-capturing robustness of, for example, weighted essentially non-oscillatory schemes, by comparing and analysing the resulting overshoots. In particular, we are able to find out the ranges of wavenumbers in which the numerical schemes are especially prone to produce overshooting oscillations. While lower dissipation is usually anticipated for high-order schemes, we provide a simple measurement for evaluating the shock-capturing robustness, which was not trivial due to the nonlinearity of shock-capturing computations.
Brchnelova, Michaela; Kuźma, Błażej; Zhang, Fan; Lani, Andrea & Poedts, Stefaan (2023). COCONUT-MF: Two-fluid ion-neutral global coronal modelling. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 678. doi: 10.1051/0004-6361/202346525. Full text in Research Archive
Kraśkiewicz, Jerzy; Murawski, Kris; Zhang, Fan & Poedts, Stefaan (2023). Monochromatic Two-Fluid Alfvén Waves in the Partially Ionised Solar Chromosphere. Solar Physics. ISSN 0038-0938. 298(1). doi: 10.1007/s11207-022-02095-1. Full text in Research Archive
Perri, Barbara; Kuźma, Błażej; Brchnelova, Michaela; Baratashvili, Tinatin; Zhang, Fan & Leitner, Peter [Show all 8 contributors for this article] (2023). COCONUT, a Novel Fast-converging MHD Model for Solar Corona Simulations. II. Assessing the Impact of the Input Magnetic Map on Space-weather Forecasting at Minimum of Activity. The Astrophysical Journal (ApJ). ISSN 0004-637X. 943(2). doi: 10.3847/1538-4357/ac9799. Full text in Research Archive
Wei, Yan-Xin; Zhang, Fan; Liu, Jun; Su, Hong-xing & Xu, Chun-guang (2023). A constrained boundary gradient reconstruction method for unstructured finite volume discretization of the Euler equations. Computers & Fluids. ISSN 0045-7930. 252. doi: 10.1016/j.compfluid.2022.105774. Full text in Research Archive
Kuźma, Błażej; Brchnelova, Michaela; Perri, Barbara; Baratashvili, Tinatin; Zhang, Fan & Lani, Andrea [Show all 7 contributors for this article] (2023). COCONUT, a Novel Fast-converging MHD Model for Solar Corona Simulations. III. Impact of the Preprocessing of the Magnetic Map on the Modeling of the Solar Cycle Activity and Comparison with Observations. The Astrophysical Journal (ApJ). ISSN 0004-637X. 942(1). doi: 10.3847/1538-4357/aca483. Full text in Research Archive
Brchnelova, Michaela; Kuźma, Błażej; Zhang, Fan; Lani, Andrea & Poedts, Stefaan (2023). The role of plasma β in global coronal models: Bringing balance back to the force. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 676. doi: 10.1051/0004-6361/202346788. Full text in Research Archive
Brchnelova, Michaela; Zhang, Fan; Leitner, Peter; Perri, Barbara; Lani, Andrea & Poedts, Stefaan (2022). Effects of mesh topology on MHD solution features in coronal simulations. Journal of Plasma Physics. ISSN 0022-3778. 88. doi: 10.1017/S0022377822000241. Full text in Research Archive
Chen, Zedong; Zhang, Fan; Liu, Jun & Chen, Biaosong (2022). A vertex-based reconstruction for cell-centered finite-volume discretization on unstructured grids. Journal of Computational Physics. ISSN 0021-9991. 451. doi: 10.1016/j.jcp.2021.110827. Full text in Research Archive
Perri, Barbara; Leitner, Peter; Brchnelova, Michaela; Baratashvili, Tinatin; Kuźma, Błażej & Zhang, Fan [Show all 8 contributors for this article] (2022). COCONUT, a Novel Fast-converging MHD Model for Solar Corona Simulations: I. Benchmarking and Optimization of Polytropic Solutions. The Astrophysical Journal (ApJ). ISSN 0004-637X. 936(1). doi: 10.3847/1538-4357/ac7237. Full text in Research Archive
Zhang, Huaibao & Zhang, Fan (2021). On the numerical overshoots of shock-capturing schemes. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 93(10), p. 3151–3159. doi: 10.1002/fld.5023. Full text in Research Archive
Zhang, Fan; Poedts, Stefaan; Lani, Andrea; Kuźma, Błażej & Murawski, Kris (2021). Two-fluid Modeling of Acoustic Wave Propagation in Gravitationally Stratified Isothermal Media. The Astrophysical Journal (ApJ). ISSN 0004-637X. 911(2). doi: 10.3847/1538-4357/abe7e8. Full text in Research Archive
Xu, Chunguang; Zhang, Fan; Dong, Haibo & Jiang, Hang (2021). Arbitrary high-order extended essentially non-oscillatory schemes for hyperbolic conservation laws. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 93(7), p. 2136–2154. doi: 10.1002/fld.4968. Full text in Research Archive
Tian, Zhuangzhuang; Wang, Guangxue; Zhang, Fan & Zhang, Huaibao (2020). A third-order compact nonlinear scheme for compressible flow simulations. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 92(10), p. 1352–1367. doi: 10.1002/fld.4831. Full text in Research Archive
Zhang, Huaibao; Zhang, Fan; Liu, Jun; McDonough, J. M. & Xu, Chunguang (2020). A simple extended compact nonlinear scheme with adaptive dissipation control. Communications in nonlinear science & numerical simulation. ISSN 1007-5704. 84. doi: 10.1016/j.cnsns.2020.105191. Full text in Research Archive
Chen, Zedong; Zhang, Fan; Liu, Jun & Chen, Biaosong (2020). An iterative near-boundary reconstruction strategy for unstructured finite volume method. Journal of Computational Physics. ISSN 0021-9991. 418. doi: 10.1016/j.jcp.2020.109621. Full text in Research Archive
Zhang, Huaibao; Wang, Guangxue & Zhang, Fan (2020). A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws. International journal of computational fluid dynamics (Print). ISSN 1061-8562. 34(3), p. 187–203. doi: 10.1080/10618562.2020.1722807. Full text in Research Archive
Dong, Haibo; Fu, Lin; Zhang, Fan; Liu, Yu & Liu, Jun (2019). Detonation Simulations with a Fifth-Order TENO Scheme. Communications in Computational Physics. ISSN 1815-2406. 25(5), p. 1357–1393. doi: 10.4208/cicp.OA-2018-0008. Full text in Research Archive
Zhang, Huaibao; Zhang, Fan & Xu, Chunguang (2019). Towards optimal high-order compact schemes for simulating compressible flows. Applied Mathematics and Computation. ISSN 0096-3003. 355, p. 221–237. doi: 10.1016/j.amc.2019.03.001. Full text in Research Archive
Dong, Haibo; Liu, Jun; Chen, Zedong & Zhang, Fan (2018). Numerical Investigation of Lateral Jet with Supersonic Reacting Flow. Journal of Spacecraft and Rockets. ISSN 0022-4650. 55(4), p. 928–935. doi: 10.2514/1.A34096. Full text in Research Archive
Zhang, Fan; Liu, Jun & Chen, Biaosong (2018). Modified multi-dimensional limiting process with enhanced shock stability on unstructured grids. Computers & Fluids. ISSN 0045-7930. 161, p. 171–188. doi: 10.1016/j.compfluid.2017.11.019. Full text in Research Archive
Dong, Haibo; Zhang, Fan; Xu, Chunguang & Liu, Jun (2018). An improved uncoupled finite volume solver for simulating unsteady shock-induced combustion. Computers & Fluids. ISSN 0045-7930. 167, p. 146–157. doi: 10.1016/j.compfluid.2018.03.001. Full text in Research Archive
Zhang, Fan; Liu, Jun; Chen, Biaosong & Zhong, Wanxie (2017). A robust low-dissipation AUSM-family scheme for numerical shock stability on unstructured grids. International Journal for Numerical Methods in Fluids. ISSN 0271-2091. 84(3), p. 135–151. doi: 10.1002/fld.4341. Full text in Research Archive
Zhang, Fan; Liu, Jun; Chen, Biaosong & Zhong, Wanxie (2016). Evaluation of rotated upwind schemes for contact discontinuity and strong shock. Computers & Fluids. ISSN 0045-7930. 134-135, p. 11–22. doi: 10.1016/j.compfluid.2016.05.010. Full text in Research Archive

View all works in NVA

Zhang, Fan (2025). Constructing reduced order models of energetic phenomena in the solar atmosphere. Full text in Research Archive
Zhang, Fan & Martínez-Sykora, Juan (2025). Multi-fluid-multi-species modeling of magnetohydrodynamics wave propagation in partially ionized plasmas. Full text in Research Archive
Zhang, Fan & Martínez-Sykora, Juan (2025). Multi-fluid-multi-species modeling of MHD waves in gravitationally-stratified partially ionized plasmas. Full text in Research Archive
Zhang, Fan (2025). Using reduced order models to reproduce magnetic reconnection: driven by MHD simulation data. Full text in Research Archive
Zhang, Fan (2025). Modal analysis and reduced order representation of solar coronal magnetic reconnection. Full text in Research Archive
Zhang, Fan; Brchnelova, Michaela; Lani, Andrea & Poedts, Stefaan (2024). Physically-consistent Riemann solvers for accurate and robust MHD modelling with low plasma beta. Full text in Research Archive
Zhang, Fan; Brchnelova, Michaela; Lani, Andrea & Poedts, Stefaan (2024). Physically-consistent Riemann solvers for accurate and robust global solar coronal modelling. Full text in Research Archive
Zhang, Fan; Brchnelova, Michaela; Lani, Andrea & Poedts, Stefaan (2024). MHD modelling of the global solar corona: numerical performance and physical consequences. Full text in Research Archive