Radiation hydrodynamics equations (RHE) refer to the study of how interactions between radiation and matter influence thermodynamic states and dynamic flow, which has been widely applied to high ...temperature hydrodynamics, such as inertial confinement fusion (ICF) and astrophysical gaseous stars. Solving RHE accurately and robustly even under the equilibrium diffusion approximation is a challenging task. To address this, we develop two types of high order conservative Lagrangian schemes for RHE in the equilibrium-diffusion limit for the two dimensional case on the Lagrangian moving mesh. Based on the multi-resolution WENO reconstruction for the spatial discretization and strong stability preserving Runge-Kutta (SSP-RK) time discretization, we first develop an explicit Lagrangian scheme with the HLLC numerical flux to achieve high order accuracy in space and time. We also discuss the positivity-preserving property of the high order explicit Lagrangian scheme. To overcome the severe time step restriction arising from the nonlinear radiation diffusion term in the explicit scheme, we further present a high order explicit-implicit-null (EIN) Lagrangian scheme. By adding a sufficiently large linear diffusion term on both sides of the scheme, we treat the complicated nonlinear parts explicitly and efficiently, and treat the added linear diffusion term on the right-hand side implicitly with a relaxed time step restriction. According to our numerical experiments, these two types of Lagrangian schemes are high order accurate, conservative and can capture the interfaces automatically. Additionally, the explicit scheme is found to be non-oscillatory and can preserve positivity while maintaining the original high order accuracy.
•Anions determines the destruction of functional groups and desulfurization capacity.•Influence of acid radical electronegativity is smaller than van der Waals force.•Anion chain length is ...proportional to the destruction of FTIR structure parameters.•Thermodynamic evolution behavior of samples is mastered.
There is an urgent need for a green and efficient inhibitor to inhibit coal spontaneous combustion (CSC). Ionic liquids (ILs) have led to a growing interest because of eco-friendliness, sustainability, and excellent designable properties. Herein, we report some ILs, which are composed of EMIM+ cations and different anions (Cl–, BF4–, OAC–, OTf–). Anions show the characteristics of increased chain length and enhanced electronegativity of acid radical. The effect of the chain volume of anions and the strength of acidity on the microstructure of coal were measured by analyzing and comparing the changes of element morphology, Fourier Transform infrared spectroscopy structure parameters, and microcrystalline in this work. The results illustrate that with the increase of the anionic chain volume and the electronegativity of acid radical, the ILs appear the outstanding ability to destroy the lamellar diameter microcrystals and the structural abundance of aliphatic hydrocarbons of coal. With the enhancement of the electronegativity of anionic acid radical, the degree of reduction of CO and COO functional groups of coal and the ability of desulfurization rate are enhanced. The thermodynamic process demonstrates that the dry cracking temperature and ignition temperature can increase by 19.3 °C and 10.0 °C, respectively, resulting in coal may be inhibited during the oxidation. In additional, the thermal kinetic behaviors of samples were investigated by Starink models. Results indicated that the apparent activation energy of the inhibited samples can be increased from 51.96 kJ mol−1 of Un-tc to EMImBF4-tc 60.52 kJ mol−1 in the stages of thermal decomposition and combustion. The regular destruction characteristics of anions and cations on coal molecules to suggest hopeful prospects ILs as a novel and designable materials in the field of prevention CSC fire.
In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed for solving compressible Euler equations. The method detects ...critical numerical fluxes which may lead to negative density and pressure, and for such critical fluxes imposes a simple flux limiter by combining the high-order numerical flux with the first-order Lax–Friedrichs flux to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.
Coal spontaneous combustion is characterized by high-temperature oxidation and microscopic mechanisms. These are essential aspects to understand when attempting to control or prevent spontaneous ...combustion. Three fresh bituminous coal samples were collected for experimentation from Huainan, China. X-ray diffraction and Fourier-transform infrared spectrometry were conducted to determine the microscopic characteristics of coal during high-temperature oxidation. The mineral structures and functional groups were ascertained to ensure that the original structural characteristics of the coals were obtained. Thermogravimetry–differential scanning calorimetry was used to divide the high-temperature oxidation into four substages and obtain detailed exothermic characteristics. The heat energy release exhibited a positive correlation with an increase in temperature.
Moreover, to investigate the relationship between the functional groups and their exothermic characteristics, correlation analysis was conducted for describing the quantitative phenomena within the four oxidation stages. The results revealed that the oxygen-containing groups were initially the most active and reactive among the 14 types of functional groups. The most rapid stage of spontaneous combustion, in which should be the most cautious and aware of risks, was the oxygen adsorption and mass gain stage because the heat energy output increased rapidly and passed this stage, thus leading to dangerous and possibly unrecoverable situations.
•TG-DSC was conducted to divide the high-temperature oxidation into four substages.•Fourteen types of functional groups were explored and elucidated in four substages.•Quantitative phenomena in four substages were described by correlation analysis.•Oxygen adsorption and mass gain stage were found as the critical stage.
In the mining of multiple coal seams, geological fracture may cause water from aquifers to accumulate in the overlying gob. Residual coal in the overlying gob after water immersion and air exposure ...is regarded as soaked coal, which is at a high risk of coal spontaneous combustion. In the present study, Fourier transform infrared spectrometry and synchronous thermal analysis were performed to investigate the active functional groups, characteristic temperatures, and exothermic properties of bituminous coal (selected due to its abundance in northwestern China) immersed in water for different durations (150, 180, 210, and 240 days). On the basis of reaction mechanism equations, two thermokinetic models were used to calculate the apparent activation energy (AAE) in different stages of coal pyrolysis. Results revealed that soaked coals were more prone to spontaneous combustion than raw coal (WW0) because of changes in the numbers of functional groups and characteristic temperatures. The critical soaking duration of 180 days increased the exothermic strength of coal to its maximum. The AAE of WW0 was higher than that of soaked coals in Stages 1 and 4 of coal pyrolysis, indicating that soaked coals were more likely to react.
•Functional groups of raw and soaked bituminous coal were analysed.•Characteristic parameters of raw and soaked bituminous coals were determined.•Bituminous coals soaked for 180 days had the highest exothermic strength.•The oxidation of soaked bituminous coals conformed to chemical reaction (n = 4).
•A high order finite difference scheme for compressible two-medium flows.•The scheme is conservative.•The new method can maintain high order accuracy when the solution is smooth.•WENO is applied to ...the primitive variables to maintain the equilibrium of velocity and pressure across the interface.
In this paper, a high order finite difference conservative scheme is proposed to solve two-medium flows. Our scheme has four advantages: First, our scheme is conservative, which is important to ensure the numerical solution captures the main features properly. Second, our scheme directly applies the WENO interpolation method to the primitive variables so that it can maintain the equilibrium of velocity and pressure across the interface, which is very helpful to obtain a non-oscillatory solution. Third, the usage of nodal values enables us to manipulate algebraic functions easily. Fourth, the scheme can maintain high order accuracy when the solution is smooth. Extensive numerical experiments are performed to verify the high resolution and non-oscillatory performance of this new scheme.
In this paper, we improve the simple WENO limiter for the Runge-Kutta discontinuous Galerkin (RKDG) method in 34 for solving two-dimensional hyperbolic systems on unstructured meshes. The major ...improvement is reducing the number of polynomials transformed to the characteristic fields for each direction. For the triangular mesh, this new simple WENO limiter transforms only two polynomials to the characteristic fields for each direction, while the original simple WENO limiter 34 uses four polynomials. Thus the improved simple WENO limiter reduces the computational cost and improves the efficiency. It provides a simpler and more practical and efficient way to the characteristic-wise limiting procedure, while still simultaneously maintaining uniform high-order accuracy in smooth regions and controlling spurious nonphysical oscillations near discontinuities. We also apply this improved simple WENO limiter to a high order method constructed for solving hyperbolic conservation laws on arbitrarily distributed point clouds 10, where polygonal meshes are constructed based on random points and the traditional DG method was adopted on the constructed polygonal mesh. For such a complex polygonal mesh, this limiter still transforms only two polynomials to the characteristic fields. Thus the simplicity and efficiency of this new limiter is more evident in this case. Numerical results are provided to illustrate the accuracy and effectiveness of this procedure. For some examples, the improved limiter has less smearing and higher resolution than the original one.
In this paper, a new type of inverse Lax-Wendroff boundary treatment is designed for high order finite difference schemes for solving general convection-diffusion equations on time-varying domain. ...This new method can achieve high order accuracy on Dirichlet boundary conditions with moving boundary. To ensure stability of the boundary treatment, we give a convex combination of the boundary treatments for the diffusion-dominated and the convection-dominated cases. A group convex combination of weights is carefully designed to avoid zero denominator, resulting in a unified algorithm for pure convection, convection-dominated, convection-diffusion, diffusion-dominated and pure diffusion cases. In order to match the time levels when constructing values of ghost points in the two intermediate stages of the third order Runge-Kutta method, we propose a new approximation to the mixed derivatives at the boundaries to ensure high order accuracy and to improve computational efficiency. In particular, we extend the boundary treatment to the compressible Navier-Stokes equations, which satisfies the isothermal no-slip wall boundary condition at any Reynolds number. We provide numerical tests for one- and two-dimensional problems involving both scalar equations and systems, demonstrating that our boundary treatment is high order accurate for problems with smooth solutions and also performs well for problems involving interactions between viscous shocks and moving rigid bodies.
•ILW boundary treatment for convection-diffusion equations on time-varying domain.•Navier-Stokes equations with isothermal no-slip wall condition on moving boundaries.•Interactions between viscous shocks and moving rigid bodies.
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