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Shallow Water Flow Modeling
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Franziska Tügel, Ilhan Özgen-Xian, Franz Simons, Aziz Hassan, Reinhard Hinkelmann
As the exact solution of the Riemann problem is computationally costly and for the flux computation in the FVM method only the solution at the sampling point x/t = 0 is needed, approximate Riemann solvers have been developed, where the Harten-Lax-van Leer (HLL), the Harten-Lax-van Leer-Contact (HLLC), which in contrast to the HLL solver also restores the contact wave, and the Roe solver are the most common ones. In the presented studies, the HLLC Riemann solver is used; a detailed derivation of the HLLC solver can be found in Simons (2020).
Compressible Flow
Published in M. Necati Özişik, Helcio R.B. Orlande, Marcelo José Colaço, Renato Machado Cotta, Finite Difference Methods in Heat Transfer, 2017
M. Necati Özişik, Helcio R.B. Orlande, Marcelo José Colaço, Renato Machado Cotta
For the approximate Riemann solver, we follow Toro (1999) and use the HLLC scheme, which is a modification of the HLL scheme proposed by Harten, Lax, and van Leer. Details are avoided here because they can be found in Toro (1999). In the HLLC scheme, the approximations for U*E and U*D are given by
Development of a Lagrangian–Eulerian approach-based five-equation two-fluid model for simulation of multiphase reactive flows
Published in Numerical Heat Transfer, Part B: Fundamentals, 2023
First, the five-equation multiphase model is chosen to simulate the flow over a side jet problem. The ATM-type HLLC Riemann solver is used. To clearly capture the movement of the side jet, a computational domain is used for this test case. We have refined the grids around the injector to resolve the injection details in this complex problem. The test condition was as same as the experiment done by Lin et al. [51]. The freestream of supersonic flow with a velocity of The pressure was The injector was located at The inject velocity of the liquid jet was To achieve the pressure equilibrium between liquid jet and the gas phase, sometimes the in the stiffened gas equation of state (12) makes the flow pressure become negative in the simulation. For this reason, we will not apply the turbulence model in this case.
A Divergence-Free High-Order Spectral Difference Method with Constrained Transport for Ideal Compressible Magnetohydrodynamics
Published in International Journal of Computational Fluid Dynamics, 2021
Up to now, the SD method has contributed to the astrophysical community in terms of hydrodynamic simulation due to its spectral accuracy, great flexibility and suitability for high-performance computing. A massively parallel Compressible High-Order Unstructured Spectral difference (CHORUS) code was developed by Wang, Liang, and Miesch (2015) for simulating stratified convection in rotating spherical shells. This code was later applied to performing global 3D simulations of thermal convection in oblate solar-type stars (Wang, Miesch, and Liang 2016). But the CHORUS code only includes hydrodynamic simulation part. In our previous efforts, the MHD version of the CHORUS code based on a Generalised Lagrange Multiplier (GLM) divergence cleaning approach were built (Yang and Liang 2018; Zhang and Liang 2020). However, when it was applied to solar convection simulation which spans a long time period, the accumulation of the error gradually drove the solution to blow up (Zhang 2019). Moreover, in the GLM-MHD formulation, ad hoc parameters are difficult to adjust. A novel high-order SD method for the induction equation proposed by Veiga in (2021) might be useful for avoiding these problems. This new SD method is a high-order extension of the original CT method built on the staggered grids. It distributes solution points of , and in a staggered fashion, which is different from traditional SD method. Due to this special distribution, one major difficulty to extend it to the ideal MHD equations is to solve 2D Riemann problems at nodal points or element edges. But designing an accurate and robust 2D Riemann solver in the context of ideal MHD can be challenging. The current study hopes to avoid designing 2D Riemann solvers but still preserve advantages of the CT method, e.g. involving no problem-dependent tuning parameters and preserving the discrete to the accuracy of machine round-off error. The proposed method should be stable and accurate for long time integration. Thus it can offer great flexibility and robustness for predicting challenging MHD flows from the astrophysical background, e.g. three-dimensional solar flares.