Feature-driven Cartesian adaptive mesh refinement for vortex-dominated flows

We develop locally normalized feature-detection methods to guide the adaptive mesh refinement (AMR) process for Cartesian grid systems to improve the resolution of vortical features in aerodynamic wakes. The methods include: the Q-criterion [1], the λ₂ method [2], the λ_ci method [3], and the λ₊ method [4]. Specific attention is given to automate the feature identification process by applying a local normalization based upon the shear-strain rate so that they can be applied to a wide range of flow-fields without the need for user intervention. To validate the methods, we assess tagging efficiency and accuracy using a series of static vortex-dominated flow-fields, and use the methods to drive the AMR process for several theoretical and practical simulations. We demonstrate that the adaptive solutions provide comparable accuracy to solutions obtained on uniformly refined meshes at a fraction of the computational cost. Overall, the normalized feature detection methods are shown to be effective in driving the AMR process in an automated and efficient manner.     

Compact integration factor methods for complex domains and adaptive mesh refinement

Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction–diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinates, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction–diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed.     

Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement

Block-structured meshes provide the ability to concentrate grid points and computational effort in interesting regions of a flow field, without sacrificing the efficiency and low memory requirements of a regular grid. We describe an algorithm for simulating radiation diffusion on such a mesh, coupled to multi-fluid gasdynamics. Conservation laws are enforced by using locally conservative difference schemes along with explicit synchronization operations between different levels of refinement. In unsteady calculations each refinement level is advanced at its own optimal timestep. Particular attention is given to the appropriate coupling between the fluid energy and the radiation field, the behavior of the discretization at sharp interfaces, and the form of synchronization between levels required for energy conservation in the diffusion process. Two- and three-dimensional examples are presented, including parallel calculations performed on an IBM SP-2.     

A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics

Adaptive mesh refinement (AMR) in conjunction with high order upwind finite difference methods has been used effectively on a variety of problems. In this paper we discuss an implementation of an AMR finite difference method that solves the equations of gas dynamics with two material species in three dimensions. An equation for the evolution of volume fractions augments the gas dynamics system. The material interface is preserved and tracked from the volume fractions using a piecewise linear reconstruction technique.     

A new electromagnetic particle-in-cell model with adaptive mesh refinement for high-performance parallel computation

A new electromagnetic particle-in-cell (EMPIC) model with adaptive mesh refinement (AMR) has been developed to achieve high-performance parallel computation in distributed memory system. For minimizing the amount and frequency of inter-processor communications, the present study uses the staggering grid scheme with the charge conservation method, which consists only of the local operations. However, the scheme provides no numerical damping for electromagnetic waves regardless of the wavenumber, which results in significant noise in the refinement region that eventually covers over physical signals. In order to suppress the electromagnetic noise, the present study introduces a smoothing method which gives numerical damping preferentially for short wavelength modes. The test simulations show that only a weak smoothing results in drastic reduction in the noise, so that the implementation of the AMR is possible in the staggering grid scheme. The computational load balance among the processors is maintained by a new method termed the adaptive block technique for the domain decomposition parallelization. The adaptive block technique controls the subdomain (block) structure dynamically associated with the system evolution, such that all the blocks have almost the same number of particles. The performance of the present code is evaluated for the simulations of the current sheet evolution. The test simulations demonstrate that the usage of the adaptive block technique as well as the staggering grid scheme enhances significantly the parallel efficiency of the AMR-EMPIC model.     

Excess molar volumes of ternary mixtures {n-butylacetae + 1-butanol + 1, 2-butanediol} and {n-butylacetate + 1-butanol + 1, 3-butanediol} at T = 303.15 K

Excess molar volumes of the ternary systems formed by {n-butylacetate + 1-butanol + 1,2-butanediol } and {n-butylacetate + 1-butanol + 1,3-butanediol} were measured at 303.15 K for the whole composition range. The excess molar volumes, V_m^E, for binary mixtures of {n-butylacetate + 1-butanol, + 1,2-butanediol and + 1,3-butanediol} are positive and for the binary mixtures of {1-butanol + 1,2-butanediol and + 1,3-butanediol} are negative. Several empirical expressions are used to predict and correlate the ternary excess molar volumes from experimental results on the constituted binaries and analyzed to gain insight about liquid mixture interactions.     

Modeling material responses by arbitrary Lagrangian Eulerian formulation and adaptive mesh refinement method

In this paper we report an efficient numerical method combining a staggered arbitrary Lagrangian Eulerian (ALE) formulation with the adaptive mesh refinement (AMR) method for materials modeling including elastic–plastic flows, material failure, and fragmentation predictions. Unlike traditional AMR applied on fixed domains, our investigation focuses on the application to moving and deforming meshes resulting from Lagrangian motion. We give details of this numerical method with a capability to simulate elastic–plastic flows and predict material failure and fragmentation, and our main focus of this paper is to create an efficient method which combines ALE and AMR methods to simulate the dynamics of material responses with deformation and failure mechanisms. The interlevel operators and boundary conditions for these problems in AMR meshes have been investigated, and error indicators to locate material deformation and failure regions are studied. The method has been applied on several test problems, and the solutions of the problems obtained with the ALE–AMR method are reported. Parallel performance and software design for the ALE–AMR method are also discussed.     

Optimally gain-flattened and dispersion-managed C + L-band hybrid amplifier using a single-wavelength pump laser

We propose a hybrid C-band erbium-doped fiber amplifier (EDFA) and L-band Raman fiber amplifier (RFA) using a single pump laser diode. The optimum pump sharing ratio to EDFA/RFA is 1/10 with a total pump power of 660 mW. Using multiple fiber Bragg gratings (FBGs) with various reflectivities at different positions along the dispersion compensation fiber, the optimum dispersion compensation and power equalization for C + L-band channels are simultaneously realized. With an input power of −20 dBm/ch, the signal power variation among the channels is reduced from 9.8 dB to less than ±0.5 dB. Two pump reflectors are introduced to increase the pumping efficiency.     

Volumetric and viscosity behaviors of the chromic anhydride + sodium dichromate + sodium chromate + water from (298.15 to 333.15) K

The densities and viscosities of chromic anhydride + sodium dichromate + sodium chromate + water quaternary mixtures and sodium dichromate + sodium chromate + water ternary mixtures have been measured at the temperatures(298.15, 303.15, 313.15, 323.15 and 333.15)K. The experimental data were correlated with the Vogel–Tamman–Fulcher equation. The apparent molar volumes, limiting partial molar volumes and viscosity B-coefficient of chromic anhydride were calculated from the experimental measurements. The solute–solute interactions, solute-mixed solvent interactions and the structural-making effect of chromic anhydride have been discussed using Hepler criterion and Jones–Dole equation.     

Near-barrier fusion, breakup and scattering for the Be + Sm system

Fusion, breakup and scattering for the ⁹Be + ¹⁴⁴Sm system at near barrier energies are investigated by different approaches. We show that at energies above the barrier there is a small complete fusion suppression when compared with predictions from a double folding potential and with a similar tightly bound system. At sub-barrier energies there is no significant deviation from the predictions using coupled channel calculations that do not include the breakup channel. The energy dependence of the optical potential does not show the usual threshold anomaly found in tightly bound systems. From a simultaneous analysis of fusion and scattering data we estimate the distance where breakup starts to occur.     

A quantitative explanation for the apparent anomalous temperature dependence of OH + HO2 = H2O + O2 through multi-scale modeling

Kinetic models for complex chemical mechanisms are comprised of tens to thousands of reactions with rate constants informed by data from a wide variety of sources – rate constant measurements, global combustion experiments, and theoretical kinetics calculations. In order to integrate information from distinct data types in a self-consistent manner, a framework for combustion model development is presented that encapsulates behavior across a wide range of chemically relevant scales from fundamental molecular interactions to global combustion phenomena. The resulting kinetic model consists of a set of theoretical kinetics parameters (with constrained uncertainties), which are related through kinetics calculations to temperature/pressure/bath-gas-dependent rate constants (with propagated uncertainties), which in turn are related through physical models to combustion behavior (with propagated uncertainties). Direct incorporation of theory in combustion model development is expected to yield more reliable extrapolation of limited data to conditions outside the validation set, which is particularly useful for extrapolating to engine-relevant conditions where relatively limited data are available. Several key features of the approach are demonstrated for the H₂O₂ decomposition mechanism, where a number of its constituent reactions continue to have large uncertainties in their temperature and pressure dependence despite their relevance to high-pressure, low-temperature combustion of a variety of fuels. Here, we use the approach to provide a quantitative explanation for the apparent anomalous temperature dependence of OH + HO₂ = H₂O + O₂ – in a manner consistent with experimental data from the entire temperature range and ab initio transition-state theory within their associated uncertainties. Interestingly, we do find a rate minimum near 1200 K, although the temperature dependence is substantially less pronounced than previously suggested.     

Volumetric properties and viscosities of the 2-pyrrolidone + 1,2-propanediol + water ternary system and its binary constituents at T = 313.15 K

Densities and viscosities of ternary mixtures of 2-pyrrolidone + 1,2-propanediol + water and corresponding binary mixtures of 1,2-propanediol + water, 2-pyrrolidone + water and 2-pyrrolidone + 1,2-propanediol have been measured over the whole composition range at 313.15 K. From the obtained data, the excess molar volumes (V^E), the deviations in viscosity (Δη) and the excess Gibbs free energy of activation (ΔG^?E) have been calculated. The V^E, Δη and ΔG^?E results were correlated and fitted by the Redlich–Kister equation for binary mixtures and by the Cibulka equation for ternary mixtures, as a function of mole fraction. Several predictive empirical relations were applied to predict the excess molar volumes of ternary mixtures from the binary mixing data.     

Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes

Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.     

An interaction potential based lattice Boltzmann method with adaptive mesh refinement (AMR) for two-phase flow simulation

The lattice Boltzmann method (LBM) for two-phase flow simulation is often hindered by insufficient resolution at the interface. As a result, the LBM simulation of bubbles in bubbling flows is commonly limited to spherical or slightly deformed bubble shapes. In this study, the adaptive mesh refinement method for the LBM is developed to overcome such a problem. The approach for this new method is based on the improved interaction potential model, which is able to maintain grid-independent fluid properties in the two-fluid phases and at the interface. The LBM–AMR algorithm is described, especially concerning the LBM operation on a non-uniform mesh and the improved interaction potential model. Numerical simulations have been performed to validate the method in both single phase and multiphase flows. The 2D and 3D simulations of the buoyant rise of bubbles are conducted under various conditions. The agreement between the simulated bubble shape and velocity with experiments illustrates the capability of the LBM–AMR approach in predicting bubble dynamics even under the large bubble deformation conditions. Further, the LBM–AMR technique is capable of simulating a complex topology change of the interface. Integration of LBM with AMR can significantly improve the accuracy and reduce computation cost. The method developed in this study may appreciably enhance the capability of LBM in the simulation of complex multiphase flows under realistic conditions.     

Crystal growth and structural properties of the spinel-type Li1 + xMn2 − xO4 (x = 0.10, 0.14)

Single crystals of the lithium-rich lithium manganese oxide spinels Li_1 + xMn_2 − xO₄ with x = 0.10 and 0.14 have been successfully synthesized in high-temperature molten chlorides at 1023 K. The single-crystal X-ray diffraction study confirmed the cubic Fd3¯m space group and the lattice parameters of a = 8.2401(9) Å for x = 0.10 and a = 8.2273(10) Å for x = 0.14 at 300 K, respectively. The crystal structures have been refined to the conventional values R = 3.7% for x = 0.10 and R = 3.1% for x = 0.14, respectively. Low-temperature single-crystal X-ray diffraction experiments revealed that these single crystal samples showed no phase transition between 100 and 300 K. The electron-density distribution images in these compounds by the single-crystal MEM analysis clearly showed strong covalent bonding features between the Mn and O atoms due to the Mn–3d and O–2p interaction.     

A posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid–solid heat transfer

We analyze a multiscale operator decomposition finite element method for a conjugate heat transfer problem consisting of a fluid and a solid coupled through a common boundary. We derive accurate a posteriori error estimates that account for all sources of error, and in particular the transfer of error between fluid and solid domains. We use these estimates to guide adaptive mesh refinement. In addition, we provide compelling numerical evidence that the order of convergence of the operator decomposition method is limited by the accuracy of the transferred gradient information, and adapt a so-called boundary flux recovery method developed for elliptic problems in order to regain the optimal order of accuracy in an efficient manner. In an appendix, we provide an argument that explains the numerical results provided sufficient smoothness is assumed.     

Adjoint-based error estimation and adaptive mesh refinement for the RANS and k–ω turbulence model equations

In this article we present the extension of the a posteriori error estimation and goal-oriented mesh refinement approach from laminar to turbulent flows, which are governed by the Reynolds-averaged Navier–Stokes and k–ω turbulence model (RANS-kω) equations. In particular, we consider a discontinuous Galerkin discretization of the RANS-kω equations and use it within an adjoint-based error estimation and adaptive mesh refinement algorithm that targets the reduction of the discretization error in single as well as in multiple aerodynamic force coefficients. The accuracy of the error estimation and the performance of the goal-oriented mesh refinement algorithm is demonstrated for various test cases, including a two-dimensional turbulent flow around a three-element high lift configuration and a three-dimensional turbulent flow around a wing-body configuration.     

Densities, excess molar volumes, and viscosities of the binary and ternary mixtures of {diethylcarbonate (1) + p-chloroacetophenone (2) + 1-hexanol (3)} at 303.15 K for the liquid region and at ambient pressure

Densities ρ, dynamic viscosities η, of the ternary mixture (diethylcarbonate + p-chloroacetophenone + 1-hexanol) and the involved binary mixtures (diethylcarbonate + p-chloroacetophenone), (diethylcarbonate + 1-hexanol), and (p-chloroacetophenone + 1-hexanol) have been measured over the whole composition range at 303.15 K for the liquid region and at ambient pressure. The data obtained are used to calculate excess molar volumes V_m^E, excess partial molar volumes V¯_m,i^E, limiting excess partial molar volumes V¯_m,i^E,∞, and viscosity deviations Δη, of the binary and ternary mixtures. The data of excess molar volumes of the binary systems were fitted to the Redlich–Kister equation while for the ternary system the Cibulka equation was used. The McAllister's four body, and Kalidas and Laddha interaction models are used to correlate the kinematic viscosities of binary and ternary mixtures, respectively, to determine the fitting parameters and the standard deviations. The experimental data of the constitute binaries and ternary are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.     

Kinetics and thermochemistry of the unusual [2π + 2σ + 2σ]‐cycloaddition of quadricyclane with some dienophiles

Kinetic parameters of the unusual [2π + 2σ + 2σ]‐cycloaddition reactions of quadricyclane ( 1 ) with tetracyanoethylene ( 2 ), 4‐phenyl‐1,2,4‐triazoline‐3,5‐dione ( 3 ), N‐phenylmaleimide ( 4 ), and diethyl azodicarboxylate ( 5 ) are determined experimentally. Additionally, the enthalpies of 1  +  2 reaction in 1,4‐dioxane solution (?236.6 ± 1.0 kJ mol^?1) and 1  +  3 reaction in toluene (?255.0 ± 2.8 kJ mol^?1) are determined calorimetrically and shown to be the largest in absolute magnitude among all known cycloaddition reactions involving these dienophiles. Solvent effect on the rate of 1 + 3 reaction in 11 solvents is studied and found to be moderate and similar to that of the conventional Diels‐Alder and ene reactions. The difference in the reaction rate constants of 1 with different dienophiles can be up to 9 orders of magnitude and is mainly caused by the difference in activation enthalpies. This difference is not correlated with the standard enthalpies of reactions and is likely the result of high sensitivity of the [2π + 2σ + 2σ] reaction rates to the energy of donor‐acceptor interactions between the reactants.