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Partially‐decoupled upwind‐based total‐variation‐diminishing (TVD) finite‐difference schemes for the solution of the conservation laws governing two‐dimensional non‐equilibrium vibrationally relaxing and chemically reacting flows of thermally‐perfect gaseous mixtures are presented. In these methods, a novel partially‐decoupled flux‐difference splitting approach is adopted. The fluid conservation laws and species concentration and vibrational energy equations are decoupled by means of a frozen flow approximation. The resulting partially‐decoupled gas‐dynamic and thermodynamic subsystems are then solved alternately in a lagged manner within a time marching procedure, thereby providing explicit coupling between the two equation sets. Both time‐split semi‐implicit and factored implicit flux‐limited TVD upwind schemes are described. The semi‐implicit formulation is more appropriate for unsteady applications whereas the factored implicit form is useful for obtaining steady‐state solutions. Extensions of Roe's approximate Riemann solvers, giving the eigenvalues and eigenvectors of the fully coupled systems, are used to evaluate the numerical flux functions. Additional modifications to the Riemann solutions are also described which ensure that the approximate solutions are not aphysical. The proposed partially‐decoupled methods are shown to have several computational advantages over chemistry‐split and fully coupled techniques. Furthermore, numerical results for single, complex, and double Mach reflection flows, as well as corner‐expansion and blunt‐body flows, using a five‐species four‐temperature model for air demonstrate the capabilities of the methods.

The purpose of this paper is to identify the areas and logic of integration of different stakeholders using different methods and to analyse their applicability and challenges in practical projects. The main aim is to describe how these different methods impact value creation.

Action design research was carried out in a large hospital construction project where the first author acted as an “involved researcher” and the second author acted as an “outside researcher”. Two workshops were organised to evaluate the direct and indirect challenges and benefits of the applied four methods and to explain how different methods enable value creation.

All the studied methods provide good results in terms of usability and commitment to the aims of the project, thus delivering the direct benefits expected. Process, people and tools logic works well in this case project when applying the methods properly. Significant evidence was provided on secondary deliverables of the methods, and all analysed methods had a significant impact in the area of leading people, clarifying what “focus on people” means and how it is enabled.

Focus on people can be achieved through different operative methods if applied in the right way. It is necessary to select the most suitable methods based on all the direct and indirect deliverables.

This case project offered a platform to analyse integration methods in a real-life project using the collaborative contract method. The authors were able to participate in the analysis by taking action from the very beginning of the project in terms of training, learning, continuous development and coaching of these methods and evaluating the applicability.

This paper aims to construct a sixth-order weighted essentially nonoscillatory scheme for simulating the nonlinear degenerate parabolic equations in a finite difference framework.

To design this scheme, we approximate the second derivative in these equations in a different way, which of course is still in a conservative form. In this way, unlike the common practice of reconstruction, the approximation of the derivatives of odd order is needed to develop the numerical flux.

The results obtained by the new scheme produce less error compared to the results of other schemes in the literature that are recently developed for the nonlinear degenerate parabolic equations while requiring less computational times.

This research develops a new weighted essentially nonoscillatory scheme for solving the nonlinear degenerate parabolic equations in multidimensional space. Besides, any selection of the constants (sum equals one is the only requirement for them), named the linear weights, will obtain the desired accuracy.

A comparison of the accuracy of the central discretization scheme with artificial dissipation and the upwind flux‐difference TVD scheme has been made for the compressible Navier‐Stokes equations for high Reynolds number flows. First, a comparison is made on two one‐dimensional model problems. Then the schemes are compared on flat plate boundary layer flow. It is shown that a central scheme basically has poor accuracy due to the isotropic nature of the artificial dissipation. An upwind scheme decomposes the flow into different components and adapts the dissipation to the velocity of the components. The associated ansitropic dissipation results in a good accuracy. It is further discussed how a central discretization scheme with artificial dissipation can be improved at the expense of the same complexity of an upwind scheme.

The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme.

The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method.

Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media.

The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible.

The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers.

The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

The performance of a spinning secant‐ogive‐cylinder‐boattail projectile in the transonic regime in terms of aerodynamic drag has been analyzed numerically in this study. To obtain an accurate prediction of the spinning effect on individual drag components and total drag of a projectile for the shell design, the implicit, diagonalied, symmetric Total Variation Diminishing (TVD) scheme, accompanied by a suitable grid, is employed to solve the thin‐layer axisymmetric Navier‐Stokes equations associated with the Baldwin‐Lomax turbulence model. The computed results show that, in comparison with the non‐spinning case, to increase the spin rate can result in increases in viscous drag and nose pressure drag, but can cause decreases in boattail drag and base drag. The variations of these drag components result in only a small (less than 5%) increase in total drag; thus the performance of the transonic projectiles is found to be insensitive to the spin rate.

We present results of a mathematical model for the gas flow in an internal combustion engine consisting of a single cylinder with an inlet and outlet pipe. In order to achieve optimal performance of the engine the dependence of the gas flow on physical parameters such as pipe dimensions and valve geometry need to be understood. A system of ordinary differential equations (in time t) with discontinuous right‐hand side describes the gas properties in the cylinder, whereas the gas flow in each pipe is modelled by the Euler equations, a system of hyperbolic partial differential equations. The explicit method of Euler and a TVD scheme are used for solving these equations. However, since the coupling of the pipe equations with the o.d.e. system in the cylinder on one side and atmospheric gas properties on the other appeared to be a main problem, we concentrate on appropriate coupling conditions. The numerical techniques involve discretization in space and time, and we present different methods of discrete coupling. As a main result we show that the various coupling methods lead to quite different numerical solutions. Therefore, a careful treatment of the coupling conditions is crucial.

The discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the hyperbolic conservation law. However, it requires a significant amount of computing resources. Therefore, this paper aims to investigate how to solve the Euler equations in parallel systems and improve the parallel performance.

Discontinuous Galerkin discretization is used for the compressible inviscid Euler equations. The multi-level domain decomposition strategy was used to deal with the computational grids and ensure the calculation load balancing. The total variation diminishing (TVD) Runge–Kutta (RK) scheme coupled with the multigrid strategy was employed to further improve parallel efficiency. Moreover, the Newton Block Gauss–Seidel (GS) method was adopted to accelerate convergence and improve the iteration efficiency.

Numerical experiments were implemented for the compressible inviscid flow problems around NACA0012 airfoil, over M6 wing and DLR-F6 configuration. The parallel acceleration is near to a linear convergence. The results indicate that the present parallel algorithm can reduce computational time significantly and allocate memory reasonably, which has high parallel efficiency and speedup, and it is well-suited to large-scale scientific computational problems on multiple instruction stream multiple data stream model.

The parallel DGFEM coupled with TVD RK and the Newton Block GS methods was presented for hyperbolic conservation law on unstructured meshes.

The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws.

The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax–Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge–Kutta method.

The parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach.

The resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value.

So far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used.

This work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term experience in applied mathematics for industrial applications and the other in a starting process of international academic insertion. In this way, this scientific partnership has the potential of promoting further knowledge exchange, involving students and other collaborators.

The proposed methodology (use of OpenMP programming model for the wavelet adaptive splitting scheme) is original and contributes to a very active research area in the past years, namely, adaptive methods for conservation laws and their parallel formulations, which is of great interest for the entire scientific community.

The traditional construction delivery method is challenged by low trust and collaboration issues, resulting in increased project costs. The integrated project delivery (IPD) method is developed, through a contractual agreement, to overcome these challenges by creating a common set of terms, expectations and project goals.

A singular construction case was followed during a four-month period. Data collection consisted of contract documents and a series of semi-structured interviews with representatives from the owner, design-group and contractors.

The IPD contract was found to have a number of positive effects; it improved project behavior (e.g. trust, collaboration and communication), increased ownership among project participants and improved buildability of the design, leading to fewer surprises and interruptions in the construction phase. The study also revealed a number of challenges including contractual and legal challenges and involving too many participants in the early phases. Moreover, co-location was identified as a particular important supporting element, to build relations and improve collaboration.

This research identified lessons learned from the application, as well as initial barriers and persistent barriers for implementing IPD. To improve IPD application the top three lessons were as follows: 1) the contractual documents should be adapted and signed at an early stage as this increases financial transparency, 2) cost estimates should be carried as an iterative process and project main concept be freezed at an early stage to increase understanding and minimize risks, 3) only the most important project developers should be involved in the early phases, to avoid going into detailed design issues before the main concept is completed.