One-dimensional Scheme Research Articles

Impact of Flood on a Simple Masonry Building

AbstractIn this paper, the impact action of a flood on rural mountain buildings is systematically studied. First, based on the one-dimensional Saint-Venant water equation explicit-difference scheme, a new explicit-difference scheme is deduced to establish the evolutionary routing model of a flood. A computational formula about the impact loading of the flood model is deduced. Secondly, an impact experiment of a flood on buildings is carried out in a large wave-current tank. The heights of the water are 0.6, 0.9, and 1.2 m, and the distances between the building and floodgate are 3, 6, and 9 m, respectively. The model scale of the buildings is 1:6, and three buildings with different ratios of holes are designed to simulate the buildings in countries and villages. Based on the experimental results, the effects of the heights of the water, the distances between buildings and floodgates, and the ratios of holes on the impacting pressure are investigated. The numerical results are compared with the experimenta...

The improvement of the one-dimensional Mellor-Yamada and K-profile parameterization turbulence schemes with the non-breaking surface wave-induced vertical mixing

Both the level 2.5 Mellor-Yamada turbulence closure scheme (MY) and K-profile parameterization (KPP) are popularly used by the ocean modeling community. The MY and the KPP are improved through including the non-breaking surface wave-induced vertical mixing (Bv), and the improved schemes were tested by using continuous data at the Papa ocean weather station (OWS) during 1961–1965. The numerical results showed that the Bv can make the temperature simulations fit much better with the continuous data from Papa Station. The two improved schemes overcame the shortcomings of predicting too shallow upper mixed layer depth and consequently overheated sea surface temperature during summertime, which are in fact common problems for all turbulence closure models. Statistical analysis showed that the Bv effectively reduced the mean absolute error and root mean square error of the upper layer temperature and increased the correlation coefficient between simulation and the observation. Furthermore, the performance of vertical mixing induced by shear instability and the Bv is also compared. Both the temperature structure and its seasonal cycle significantly improved by including the Bv, regardless of whether shear instability was included or not, especially for the KPP mixing scheme, which suggested that Bv played a dominant role in the upper ocean where the mean current was relatively weak, such as at Papa Station. These results may provide a clue to improve ocean circulation models.

On one-dimensional arbitrary high-order WENO schemes for systems of hyperbolic conservation laws

In this paper, a one-dimensional case for an arbitrary high-order non-oscillatory finite-volume scheme is considered. This is an adaptation of the schemes presented in Dumbser and Kaser (J Comput Phys. 221:693–723, 2007). An entire polynomial inside each control volume is reconstructed in terms of hierarchical orthogonal polynomial bases over a reference element. A new numerical inter-cell flux function at the element interfaces is proposed. To validate the approach, several one-dimensional test problems with discontinuous solutions are computed. The results show an improvement on the non-oscillatory shock-capturing properties based on the new approach.

Flux-splitting schemes for parabolic equations with mixed derivatives

Difference schemes of required quality are often difficult to construct as applied to boundary value problems for parabolic equations with mixed derivatives. Specifically, difficulties arise in the design of monotone difference schemes and unconditionally stable locally one-dimensional splitting schemes. In parabolic problems, certain opportunities are offered by restating the problem in question so that the quantities to be determined are fluxes (directional derivatives). The original problem is then rewritten as a boundary value one for a system of equations in flux variables. Weighted schemes for parabolic equations in flux coordinates are examined. Unconditionally stable locally one-dimensional flux schemes that are first- and second-order accurate in time are constructed for a parabolic equation without mixed derivatives. A feature of systems in flux variables for equations with mixed derivatives is that the terms with time derivatives are coupled with each other.

LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

AbstractThe local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrödinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrödinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis.

Near-perfect absorber with ultrawide bandwidth in infrared region using a periodically chirped structure

We propose a near-perfect absorber with ultrawide bandwidth in infrared region using a periodically chirped subwavelength structure implemented in both one-dimensional (1D) and two-dimensional (2D) schemes. The structure is composed of an array of chirped metal–insulator–metal resonators made of a metal/dielectric two-layer grating sitting on a uniform metal layer. Each resonator harvests the photon via the SPP localization at its own resonance wavelength which exhibits linear distribution due to the linearly chirped structure. A near-perfect absorption in wide bandwidth is realized with an appropriate design under the restriction of phase-matching and subwavelength dimension. A stop-band with a FWHM of 3μm at central wavelength of ∼9μm and a high absorption efficiency of up to 92% is achieved simultaneously. This provides a novel method in designing and implementing flexible thin-film devices with wide bandwidth and high absorption efficiency.

High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs

We consider the problem of Lagrange polynomial interpolation in high or countably infinite dimension, motivated by the fast computation of solutions to partial differential equations (PDEs) depending on a possibly large number of parameters which result from the application of generalised polynomial chaos discretisations to random and stochastic PDEs. In such applications there is a substantial advantage in considering polynomial spaces that are sparse and anisotropic with respect to the different parametric variables. In an adaptive context, the polynomial space is enriched at different stages of the computation. In this paper, we study an interpolation technique in which the sample set is incremented as the polynomial dimension increases, leading therefore to a minimal amount of PDE solving. This construction is based on the standard principle of tensorisation of a one-dimensional interpolation scheme and sparsification. We derive bounds on the Lebesgue constants for this interpolation process in terms of their univariate counterpart. For a class of model elliptic parametric PDE’s, we have shown in Chkifa et al. (Modél. Math. Anal. Numér. 47(1):253–280, 2013) that certain polynomial approximations based on Taylor expansions converge in terms of the polynomial dimension with an algebraic rate that is robust with respect to the parametric dimension. We show that this rate is preserved when using our interpolation algorithm. We also propose a greedy algorithm for the adaptive selection of the polynomial spaces based on our interpolation scheme, and illustrate its performance both on scalar valued functions and on parametric elliptic PDE’s.

A Method for Solving a Conjugate Problem of Heat Transfer. Part 1

Based on the integral Laplace transform, the method of quasi-linearization, and the locally one-dimensional scheme of splitting into spatial variables, an approximate analytical solution of a conjugate problem of heat transfer in the three-dimensional formulation has been obtained.

Formation of pyrrolidinium fatty acid soap and its lyotropic liquid crystalline phase behavior

The hydrogen bond induced acid–soap like complex has been prepared from a nitrogen-containing heterocyclic compound, pyrrolidine, and the myristic acid (MA). The complex composition and the intermolecular actions between two component molecules have been characterized with techniques of nuclear magnetic resonance (NMR), X-ray diffraction (XRD) and Fourier transformation infra-red (FTIR) spectroscopy. The molar ratio between the soap (pyrrolidium myristate, PM) and the acid (MA) is identified as 1:1. As an important driving force of assembly, the existence of hydrogen bond is further confirmed by a molecular mechanics calculation. It is interesting that such an acid–soap complex (PM–MA) exhibits amphiphilicity and its lyotropic liquid crystal phase in water has been observed over a wide concentration range. A lamellar phase structure is established using the polarized optical microscopy (POM) and small-angle X-ray scattering (SAXS) measurements. The change of lattice spacing indicates a typical one-dimensional swelling scheme for the uptake of water by this lamellar phase. The frequency-independent storage and loss module could be found for these lamellar samples by rheological measurements, reflecting a highly viscoelastic nature. The obtained results should add new insights to better understand the structure and aqueous behavior of long-chain fatty acid–soaps with a large size nitrogen-heterocyclic counterion.

Splitting schemes for hyperbolic heat conduction equation

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat fluxes. In this paper we construct for the hyperbolic heat conduction equation the additive schemes of splitting with respect to directions. Unconditional stability of locally one-dimensional splitting schemes is established. New splitting schemes are proposed and studied for a system of equations written in terms of the temperature and heat fluxes.

Accurate Pricing of Continuous Barrier Options With Local Volatility

In this paper we develop accurate technics to price continuous barrier options using a one-dimensional finite difference scheme, allowing for time-dependent drift as well as time- and state-dependent volatilities. We provide numerical examples which demonstrate the smoothness and accuracy of such methods in the Black-Scholes context as well as in the Dupire Local Volatility model.

홀로그래픽 저장장치를 위한 2차원 SOVA 성능 비교

본 논문에서는 홀로그래픽 저장장치를 위한 2차원 검출기인 2차원 SOVA와 반복 검출 2차원 SOVA의 검출 성능을 비교하였다. 홀로그래픽 저장장치는 2차원 인접심볼간 간섭이 있는 채널을 가지고 있어서 2차원 검출기를 사용하여야 검출 성능이 좋다. 2차원 SOVA와 반복 검출 2차원 SOVA는 2차원 인접심볼간 간섭이 있는 채널에서 잘 동작하는 검출기이다. 이 두가지 검출기를 분석하고 성능을 비교해 보았다. 2차원 SOVA는 1차원 검출기에 비해 약 2 dB의 성능이득이 있었고, 반복 검출 2차원 SOVA는 2차원 SOVA에 비해 약 1 dB 정도의 성능 이득이 있었다. 반대로, 반복 검출 2차원 SOVA는 2차원 SOVA에 비해 약 2배 정도 복잡도가 늘어나며, 2차원 SOVA도 1차원 검출기에 비해 약 2배 정도 복잡도가 늘어난다. We introduce two-dimensional soft output Viterbi algorithm (2D SOVA) and iterative 2D SOVA for holographic data storage. Since the holographic data storage is 2D intersymbol interference (ISI) channel, the 2D detection schemes have good performance at holographic data storage. The 2D SOVA and iterative 2D SOVA are 2D detection schemes. We introduce and compare the two 2D detection schemes. The 2D SOVA is approximately 2 dB better than one-dimensional (1D) detection scheme, and iterative 2D SOVA is approximately 1 dB better than the 2D SOVA. In contrast, the iterative 2D SOVA is approximately twice complex higher than 2D SOVA, and 2D SOVA is approximately twice complex higher than 1D detection scheme.

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases

AbstractWith discretized particle velocity space, a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case [J. Comput. Phys., vol. 229 (2010), pp. 7747-7764]. For the kinetic equation, to extend a one-dimensional scheme to multidimensional flow is not so straightforward. The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional, rather than axially symmetric, in velocity space. In this paper, a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented. Instead of particle-based modeling for the rarefied flow, such as the direct simulation Monte Carlo (DSMC) method, the philosophical principal underlying the current study is a partial-differential-equation (PDE)-based modeling. Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different, the gas evolution in a discretized space is modeled with the help of kinetic equation, instead of directly solving the partial differential equation. Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface, the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions. In comparison with the DSMC and Navier-Stokes flow solvers, the current method is much more efficient than DSMC in low speed transition and continuum flow regimes, and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes. As a result, the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation. This paper will extensively evaluate the performance of the unified scheme from free molecule to continuum NS solutions, and from low speed micro-flow to high speed non-equilibrium aerodynamics. The test cases clearly demonstrate that the unified scheme is a reliable method for the rarefied flow computations, and the scheme provides an important tool in the study of non-equilibrium flow.

Towards a classification of modular compactifications of $\mathcal {M}_{g,n}$

The moduli space of smooth curves admits a beautiful compactification $\mathcal{M}_{g,n} \subset \overline{\mathcal{M}}_{g,n}$ by the moduli space of stable curves. In this paper, we undertake a systematic classification of alternate modular compactifications of $\mathcal{M}_{g,n}$ . Let $\mathcal{U}_{g,n}$ be the (non-separated) moduli stack of all n-pointed reduced, connected, complete, one-dimensional schemes of arithmetic genus g. When g=0, $\mathcal{U}_{0,n}$ is irreducible and we classify all open proper substacks of $\mathcal{U}_{0,n}$ . When g≥1, $\mathcal{U}_{g,n}$ may not be irreducible, but there is a unique irreducible component $\mathcal{V}_{g,n} \subset\mathcal{U}_{g,n}$ containing $\mathcal{M}_{g,n}$ . We classify open proper substacks of $\mathcal {V}_{g,n}$ satisfying a certain stability condition.

Sequential Two-Dimensional Partial Response Maximum Likelihood Detection Scheme with Constant-Weight Constraint Code for Holographic Data Storage Systems

A sequential two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for holographic data storage (HDS) systems is proposed. We use two complexity reduction schemes, a reduced-state trellis and a constant-weight (CW) constraint. In the reduced-state trellis, the limited candidate bits surrounding the target bit are considered for the 2D PRML detector. In the CW constraint, the trellis transitions that violate the CW condition that each code-word block has only one white bit are eliminated. However, the 2D PRML detector using the complexity reduction schemes, which operates on 47 states and 169 branches, has performance degradation. To overcome performance degradation, a sequential detection algorithm uses the estimated a priori probability. By the sequential procedure, we mitigate 2D intersymbol interference with an enhanced reliability of the branch metric. Simulation results show that the proposed 2D PRML detection scheme yields about 3 dB gains over the one-dimensional PRML detection scheme.

Unconditionally Stable FDTD Method Based on LOD Scheme for Analysis of 2-D Periodic Structures

For modeling periodic structures at oblique incidence, an unconditionally stable finite-difference time-domain technique is presented by applying the locally one-dimensional (LOD) scheme to the field transformation technique. By splitting the space operator matrix in an appropriate way, the transformed Maxwell's equations can be subdivided into two sub-steps for an efficient implementation. The accuracy and efficiency of the proposed method are verified by comparing with the results of the reference [4] and the split-field method respectively.

Flux-splitting schemes for parabolic problems

To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are associated with the transition to a new formulation of the problem, where the fluxes (derivatives with respect to a spatial direction) are treated as unknown quantities. In this case, the original problem is rewritten in the form of a boundary value problem for the system of equations in the fluxes. This work deals with studying schemes with weights for parabolic equations written in the flux coordinates. Unconditionally stable flux locally one-dimensional schemes of the first and second order of approximation in time are constructed for parabolic equations without mixed derivatives. A peculiarity of the system of equations written in flux variables for equations with mixed derivatives is that there do exist coupled terms with time derivatives.

Bicompact monotonic schemes for a multidimensional linear transport equation

Bicompact difference schemes, previously proposed by the authors for linear one-dimensional transport equations are generalized to the multidimensional case by using a coordinate-wise splitting of the multidimensional problem. The scheme stencil for each of the spatial directions is minimal and consists of two points. The schemes are efficient and can be solved by the running calculation method. The proposed difference schemes have the fourth-order approximation in space variables and first- or third-order time approximation for smooth solutions. The schemes for solving multidimensional problems have inherited the monotonicity property of one-dimensional bicompact schemes. Numerical examples are given illustrating the actual accuracy order of bicompact schemes for smooth solutions and the scheme monotonicity for discontinuous solutions.

Reduction of PAH and Soot Precursors in Benzene Flames by Addition of Ethanol

A one-dimensional premixed flame model (PREMIX) and schemes resulting from the merging of validated kinetic schemes for the oxidation of the components of the present mixtures (benzene and ethanol) were used to investigate the effect of oxygenated additives on aromatic species, which are known to be soot precursors, in fuel-rich benzene combustion. The specific flames were low-pressure (45 mbar), laminar, premixed flames at an equivalence ratio of 2.0. The blended fuels were formed by incrementally adding 4% wt of oxygen (ethanol) to the neat benzene flame and by keeping the inert mole fraction (argon) and the equivalence ratio constants. Special emphasis was directed toward the causes for the concentration-dependent influence of the blends on the amount of polycyclic aromatic hydrocarbons (PAHs) formed. The effects of oxygenate addition to the benzene base flame were seen to result in interesting differences, especially regarding trends to form PAH. The modeling results indicated that the concentration of acetylene and propargyl radicals, the main PAH precursors, as well as the PAH amounts were lower in the flame of the ethanol-benzene fuel mixture than in the pure benzene flame and that all of the formed PAHs were issued from the phenyl radical. Finally, the modeling results provided evidence that the PAH reduction was a result of simply replacing "sooting" benzene with "nonsooting" ethanol without influencing the combustion chemistry of the benzene.

The Canopy Semi-analytic Pgap And Radiative Transfer (CanSPART) model: Formulation and application

We present CanSPART: a model of gap probability (Pgap) based on a simple but flexible geometric vegetation canopy structure, coupled to a one-dimensional radiative transfer scheme, to account for the effects of crown structure and trunks on vertically resolved canopy radiation fluxes. The Pgap component of the model is intended for use in inverting ground-based and airborne gap-frequency data for biometric variables, while the full CanSPART model is intended for application within a one-dimensional multilayer soil-vegetation-atmosphere-transfer model. Our approach to modelling Pgap is novel because it uses an analytic approximation to the crown porosity, which makes it computationally efficient. Further, it can accommodate any distribution of crown and trunk heights and dimensions, allowing the model to be applied to complex canopy structures with multiple layers. The Pgap model is readily rewritten in terms of a clumping factor as a function of height and angle. Simulations of Pgap(θ,z) for idealised canopies compared favourably with those of two other models: the Analytical Clumped Two-Stream (ACTS) model (Ni-Meister et al., 2010) and an adaptation of the Nilson (1999) model. We test the analytic approximation to the crown porosity, also inherent in the Nilson (1999) model, and the applicability of a single clumping factor without angle nor height dependence. Both simplifications are demonstrated to be valid. Lovell et al. (2012, this issue) provide quantitative assessment of the Pgap component of CanSPART against ground-based lidar measurements from sites spanning a range of canopy structures.The radiative-transfer part of the model is an extension of the two-stream scheme, using Pgap as input and requiring the solution of a single matrix equation. In contrast to existing modified two-stream models which use a clumping factor, we account for both the primary effect of clumping (enhanced uncollided flux intensities) and the secondary effect (enhanced interception of scattered radiation). Application of CanSPART to three contrasting Australian field sites show that Pgap, the absorption of radiation by leaves, Qleaf, and albedo are sensitive to the clumping of leaves into crowns. Except for the most sparsely vegetated site, albedo predictions were significantly too high, unless both primary and secondary effects of clumping were included. This highlights the importance of accounting for the enhanced interception of radiation scattered by leaves in a clump (relative to the unclumped case) and suggests why modified two-stream canopy radiative transfer models using a clumping factor approach may systematically underestimate Qleaf and overestimate albedo.