spectral volume method for the 2d euler equations

... Conclusions on the 1D IBMs study 59 III The 2D methods 61 16 Introduction to the 2D methods 63 CONTENTS 17 The 2D finite volume code 17.1 The data structure 17.1.1 The grid 17.1.2 The neighbors ... error on the grid size is established To conclude the 1D phase, a few methods are selected for implementation in the 2D code 2 Introduction Part III: The 2D methods The main features of the 2D finite ... differences, except for the Cut cell method which is a finite volume method Especially the treatment of the no-slip boundary condition on the immersed boundary is crucial for the success of a method, and...

Ngày tải lên: 11/07/2014, 23:20

... spectral method works well Moreover, we can also see that the lower the noise level δ is, the better the approximate effect is; the closer to the boundary x the location is, the better the approximate ... error estimate for the proposed method can be found in Section The implementation of the numerical method is explained Regularization and Error Estimate First, let u be the Fourier transform of u: ... function of the interval −ξc , ξc The solution uc x, y can be found by using the inverse Fourier transform Define the regularized solution with measured data gδ , hδ by uδ The difference between the...

Ngày tải lên: 21/06/2014, 16:20

... fixed point theorems) from the wealth of operator theory, in order to assure the existence of a unique solution of the operator equation in H or H1 In the case of linear equations, we use the following ... difference equations of three and four variables The aim of this paper is to present the generalization of this functional-analytic method for the study of linear and nonlinear partial difference equations ... region, depending on the initial conditions and the parameters of the equations, where the solution of the difference equation under consideration holds We illustrate our method in Section by...

Ngày tải lên: 23/06/2014, 00:20

... all information then available regarding the extent to which this horizontal method has been followed and the reasons for deviations from this method in the case of particular products The harmonization ... 9.4.2) so that the bottom is uppermost, and place them in the incubator (6.3) set at 37 °C for the first plating-out medium (5.2.4.1) The manufacturer's instructions shall be followed for the second ... with the test portion, then incubated at 37 °C ± °C for 18 h ± h For certain foodstuffs the use of other pre-enrichment procedures is necessary See 9.1.2 For large quantities, the buffered peptone...

Ngày tải lên: 07/03/2014, 16:20

... = 2.2 Numerical scheme The finite volume formulation imposes conservation laws in a control volume Integration of Eq (1) over a cell with the application of the Green’s theorem, gives: ∂U (4) ... Shallow water equations in the Cartesian coordinate system ( x , t ) The conservation form of the 1D non-linear shallow water equations is written as ∂U ∂F + =S (1) ∂t ∂x where U is the vector of ... recorded for comparing with the experimental data Initial Condition Similar to Synolakis's (1987) 0.5 (m) For the numerical simulation, the initial solitary wave is simulated by the solitary wave formula...

Ngày tải lên: 22/03/2014, 12:20

... nanotubes prepared by the sonoelectrochemical method using ethylene glycol were found to be highly promising for water-splitting compared with others These methods for the synthesis of highly ordered ... nanotubes The lower the band gap of the titania S.K Mohapatra et al / Journal of Catalysis 246 (2007) 362–369 nanotubes, the better the activity for water-splitting Comparing the activity of the titania ... showing the compact nanotubes and the barrier layer The above experiments show that using ultrasonic waves for anodization can reduce the synthesis time by up to 50% and increase the length of the...

Ngày tải lên: 05/05/2014, 15:26

... enhanced reactivity tension These substances also control both towards the toxicants makes them the potential the reduction rate of metal ions and the materials for the decomposition applications ... Res., 7, 4, 39-49 (2013) 41 high performance for the decomposition of the final temperature (for min); the temperature 2-CEPS was increased at rate of 20 oC/ for 13 Also, detector temperature was ... (PVP) KBr pellets method GC and GC-MS (Varian The procedure of this method is similar to the Star 3400 CX, OV-101 CW HP 80/100 2m×1.8 Co-Precipitation method The difference is the in and DB MS,...

Ngày tải lên: 06/05/2014, 08:55

... patterns of the ZnO sample synthesized at 120 ƕC for 17 h hydrothermal treatment Fig SEM images of the time-dependent evolution in the formation of 3D flower-like ZnO synthesized 18 at 120 ƕC for h ... from the semiconductor, the holes can diffuse to the surface of the semiconductor and cause oxidation of the organic dye Therefore, a high density of surface oxygen defects is beneficial for efficient ... order to further study the effects of the hydrothermal treatment temperature on the ZnO product, samples were also synthesized at 90 ºC and 150 ºC for 17 h The morphologies of the ZnO samples prepared...

Ngày tải lên: 06/05/2014, 13:26

... Fan, Jishan: On the Cauchy problems for certain Boussinesq-α equations Proc R Soc Edinburgh Sect A 140, 319–C327 (2010) [4] Chae, Dongho: Global regularity for the 2D Boussinesq equations with ... (2.13), (1.1), (1.2), (1.6) and the H -theory of the Stokes system, we arrive at u L∞ (0,T ;H ) ≤ C This completes the proof Competing interests The authors declare that they have no competing interests ... studied the Cauchy problem of certain Boussinesq−α equations in n dimensions with n = or ˙ ˙ We establish regularity for the solution under u ∈ L1 (0, T ; B ) Here B ∞,∞ ∞,∞ denotes the homogeneous...

Ngày tải lên: 18/06/2014, 22:20

... Fan, Jishan: On the Cauchy problems for certain Boussinesq-α equations Proc R Soc Edinburgh Sect A 140, 319–C327 (2010) [4] Chae, Dongho: Global regularity for the 2D Boussinesq equations with ... (2.13), (1.1), (1.2), (1.6) and the H -theory of the Stokes system, we arrive at u L∞ (0,T ;H ) ≤ C This completes the proof Competing interests The authors declare that they have no competing interests ... studied the Cauchy problem of certain Boussinesq−α equations in n dimensions with n = or ˙ ˙ We establish regularity for the solution under u ∈ L1 (0, T ; B ) Here B ∞,∞ ∞,∞ denotes the homogeneous...

Ngày tải lên: 20/06/2014, 04:20

... performed most of the practical work, planned the experiments, analyzed the data and prepared the manuscript VB participated in the preparation of the bone cores and exposure of the samples to the ... uniform overall cell death Probably this result was due to the presence of remaining salts within the bone marrow, protecting the cells from the osmotic shock The most promising treatment for the ... X-rays for 30 min, group was placed 20 cm from an UV-C light source (Osram HNS, 30 W) for 60 The last group was placed in salt-free water (purified with Mili-Q Synthesis) for h treatment The positive...

Ngày tải lên: 20/06/2014, 04:20

... after the adduction of the foot and the varus deformity of the heel has been corrected, a simple percutaneus tenotomy of the Achilles tendon is performed We prefer to perform the tenotomy in the ... stabilize the leg with knee bent The other hand is used to grasp the foot and then place the ankle into maximum dorsiflexion followed by planter flexion The exercises were performed twice a day till the ... If the deformity is unilateral, the normal foot is placed in 45 degree of external rotation The knees were left free to stretch the gastrocnemius and to provide a corrective force to the other...

Ngày tải lên: 20/06/2014, 04:20

... after the adduction of the foot and the varus deformity of the heel has been corrected, a simple percutaneus tenotomy of the Achilles tendon is performed We prefer to perform the tenotomy in the ... stabilize the leg with knee bent The other hand is used to grasp the foot and then place the ankle into maximum dorsiflexion followed by planter flexion The exercises were performed twice a day till the ... If the deformity is unilateral, the normal foot is placed in 45 degree of external rotation The knees were left free to stretch the gastrocnemius and to provide a corrective force to the other...

Ngày tải lên: 20/06/2014, 07:20

... Fan, Jishan: On the Cauchy problems for certain Boussinesq-α equations Proc R Soc Edinburgh Sect A 140, 319–C327 (2010) [4] Chae, Dongho: Global regularity for the 2D Boussinesq equations with ... (2.13), (1.1), (1.2), (1.6) and the H -theory of the Stokes system, we arrive at u L∞ (0,T ;H ) ≤ C This completes the proof Competing interests The authors declare that they have no competing interests ... studied the Cauchy problem of certain Boussinesq−α equations in n dimensions with n = or ˙ ˙ We establish regularity for the solution under u ∈ L1 (0, T ; B ) Here B ∞,∞ ∞,∞ denotes the homogeneous...

Ngày tải lên: 20/06/2014, 21:20

... holds for every θ Î (0,1) for the case ((6.4), (6.8)), and for every θ < for the case ((6.10), (6.13)) On the other hand, since ∇hDl-1(Th) ⊂ (Dl-2(Th))d holds, boundedness of the bilinear form ... of the interested species, i.e., the amount of the species per unit volume of the fluid mixture) j = j(x) is the porosity of the medium, uniformly bounded above and below by positive numbers The ... estimate are obtained for the concentration, velocity and pressure An outline of the remainder of the paper follows: In Section 2, we describe the modeling equations The DG schemes for the concentration...

Ngày tải lên: 20/06/2014, 22:20

... predenatured at 95°C for 10 min, then 55°C for 30 The particles coupled with streptavidin were added into the hybridization mixtures and incubated at 37°C for 10 and enriched in the bottom of the tube with ... adjust the pH of the mixture to 9.1 under stirring The NaHTe solution prepared in the first step was added to the reaction mixture under N protection The resultant mixture was stirred for about ... was analysized by the Statistics Package for Social Sciences (SPSS) software A p value above 0.05 was considered that there was no significant difference between the two methods The as-prepared...

Ngày tải lên: 21/06/2014, 01:20

... finish the proof of the main result, Theorem 1.9 Just as , we will use the following two lemmas The first lemma is the following integral inequality Lemma 3.1 see Let φ ∈ Δ2 ∩ ∇2 , g ∈ Lφ Rn Then for ... estimates for the general linear higher-order parabolic equations with the help of fundamental solutions and Green functions Moreover, in 11 we proved global Schauder estimates for the initial-value ... using the uniform approach as the second-order case Recently we generalized the local Lp estimates to the Orlicz space φ D2m u Q1/6 φ |ut |2 dz ≤ C dz Q1/6 φ f φ |u|2 dz dz Q1/2 1.6 Q1/2 for ut...

Ngày tải lên: 21/06/2014, 16:20

... R2 , the problem has been solved by Chae [1] When θ = 0, the Boussinesq system reduces to the well-known Navier–Stokes equations The investigation of the inviscid limit of solutions of the Navier–Stokes ... supported by the Zhejiang Innovation Project (Grant No T200905), the ZJNSF (Grant No R6090109), and the NSFC (Grant No 11171154) References [1] Chae, D: Global regularity for the 2D Boussinesq equations ... limits for the Navier–Stokes equations with Navier friction boundary conditions Nonlinearity 19, 899–918 (2006) [6] Xiao, YL, Xin, ZP: On the vanishing viscosity limit for the 3D Navier–Stokes equations...

Ngày tải lên: 21/06/2014, 17:20

... R2 , the problem has been solved by Chae [1] When θ = 0, the Boussinesq system reduces to the well-known Navier–Stokes equations The investigation of the inviscid limit of solutions of the Navier–Stokes ... supported by the Zhejiang Innovation Project (Grant No T200905), the ZJNSF (Grant No R6090109), and the NSFC (Grant No 11171154) References [1] Chae, D: Global regularity for the 2D Boussinesq equations ... limits for the Navier–Stokes equations with Navier friction boundary conditions Nonlinearity 19, 899–918 (2006) [6] Xiao, YL, Xin, ZP: On the vanishing viscosity limit for the 3D Navier–Stokes equations...

Ngày tải lên: 21/06/2014, 20:20

... decomposition theory If fixed τ > 0, there are some efforts on the global existence of smooth solutions to the system (1.1)-(1.2) for the isentropic gas or the general hyperbolic system, the interested ... media equation as the limit of the isentropic Euler equations in one space dimension Recently, Coulombel and Goudon [1] constructed the uniform smooth solutions to (1.1) in the multidimensional ... (4.13) Apply the operator Δq to the system (4.11) to get d ∂t Δ q U + A j (0)∂x j Δq U = Δq Ᏻ − j =1 τ Δq u (4.14) By performing the Fourier transform with respect to the space variable x for (4.14)...

Ngày tải lên: 22/06/2014, 19:20