Conceptual linearization of Euler governing equations to solve high speed compressible flow using a pressure‐based method

The main objective of the current work is to introduce a new conceptual linearization strategy to improve the performance of a primitive shock‐capturing pressure‐based finite‐volume method. To avoid a spurious oscillatory solution in the chosen collocated grids, both the primitive and extended methods utilize two convecting and convected momentum expressions at each cell face. The expressions are obtained via a physical‐based discretization of two inclusive statements, which are constructed via a novel incorporation of the continuity and momentum governing equations. These two expressions in turn provide a strong coupling among the Euler conservative statements. Contrary to the primitive work, the linearization in the current work respects the definitions and essence of physics behind deriving the Euler governing equations. The accuracy and efficiency of the new formulation are then investigated by solving the shock tube as a problem with moving normal and expansion waves and the converging‐diverging nozzle as a problem with strong stationary normal shock. The results show that there is good improvement in performance of the primitive pressure‐based shock‐capturing method while its superior accuracy is not deteriorated at all. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Proficiency testing in occupational and environmental health – Current practice and international initiatives for harmonisation

An increasing number of proficiency testing schemes (PT schemes) related to occupational and environmental health have been organised. Most schemes emphasise the importance of the validation of analytical results. With regards to harmonisation of the schemes, there are many differences between the schemes at many levels. These include factors concerning their relationship with legislation, national status, type and quality of proficiency testing material, analytical range and priorities for future development. Since differences between PT schemes have been recognised at the European level by organisers of PT schemes and external quality assessment schemes (EQASs) it seems appropriate to reinforce collaboration between scheme organisers in order to improve the quality of analytical performance in occupational and environmental health.     

Numerical experiments with several variant WENO schemes for the Euler equations

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.     

Response time and vendor–assembler relationship in a supply chain

Relationships between an assembler and a vendor in a supply chain are investigated in two-period models when the assembler wants to reduce response time by incentive systems. The assembler may offer myopic or farsighted incentive contracts to the vendor, under short-term or long-term relationships. Incentive schemes, effort levels, and expected payoffs under different perspectives and relationships are examined. We find that a farsighted assembler provides the vendor with a higher incentive than a myopic assembler in the first period. A long (short)-term relationship is preferred if the value of farsightedness under a long-term relationship is greater (less) than the switching option value under a short-term relationship. We propose several sufficient conditions regarding which perspectives and relationships are preferred.     

Isotropic Subspaces of Polylinear Forms

The dimensions of maximal isotropic subspaces of symmetric and skew-symmetric forms of degree d in general position are found.     

Two splitting schemes for nonstationary convection-diffusion problems on tetrahedral meshes

Two splitting schemes are proposed for the numerical solution of three-dimensional nonstationary convection-diffusion problems on unstructured meshes in the case of a full diffusion tensor. An advantage of the first scheme is that splitting is generated by the properties of the approximation spaces and does not reduce the order of accuracy. An advantage of the second scheme is that the resulting numerical solutions are nonnegative. A numerical study is conducted to compare the splitting schemes with classical methods, such as finite elements and mixed finite elements. The numerical results show that the splitting schemes are characterized by low dissipation, high-order accuracy, and versatility.     

Mortar element methods for parabolic problems

In this article a standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial‐boundary value problems. Optimal error estimates in L^∞(L²) and L^∞(H¹)‐norms for semidiscrete methods for both the cases are established. The key feature that we have adopted here is to introduce a modified elliptic projection. In the standard mortar element method, a completely discrete scheme using backward Euler scheme is discussed and optimal error estimates are derived. The results of numerical experiments support the theoretical results obtained in this article. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O(h⁴+τ⁵). It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.     

An efficient ghost fluid method for compressible multifluids in Lagrangian coordinate

In this paper, we present an extended ghost fluid method (GFM) for computations of inviscid compressible multifluids in Lagrangian coordinate. That is, we capture the appropriate interface conditions by defining a fluid that has the velocity and the pressure of the real fluid at each point, but the entropy or the internal energy of some other fluid. Meanwhile, a single-fluid solver, CWENO-type central-upwind scheme, is developed in Lagrangian coordinate. The high resolution and the non-oscillatory quality of the scheme can be verified by solving several numerical experiments.