Search results

A new approach for solving steady incompressible Navier‐Stokes equations is presented in this paper. This method extends the upwind Riemann‐problem‐based techniques to viscous flows, which is obtained by applying modified artificial compressibility Navier‐Stokes equations and fully discrete high‐order numerical schemes for systems of advection‐diffusion equations. In this approach, utilizing the local Riemann solutions the steady incompressible viscous flows can be solved in a similar way to that of inviscid hyperbolic conservation laws. Numerical experiments on the driven cavity problem indicate that this approach can give satisfactory solutions.

The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodible beds. Although such models present a real opportunity for shallow water flows over movable beds, this paper is the first to propose a multilayered solver for this class of flow problems.

Multilayered beds formed with different erodible soils are considered in this study. The governing equations consist of the well-established shallow water equations for the flow, a transport equation for the suspended sediments, an Exner-type equation for the bed load and a set of empirical equations for erosion and deposition terms. For the numerical solution of the coupled system, the authors consider a non-homogeneous Riemann solver equipped with interface-tracking tools to resolve discontinuous soil properties in the multilayered bed. The solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms.

This paper reveals that modeling shallow water flows over multilayered sedimentary topography can be achieved by using a coupled system of partial differential equations governing sediment transport. The obtained results demonstrate that the proposed numerical model preserves the conservation property, and it provides accurate results, avoiding numerical oscillations and numerical dissipation in the approximated solutions.

A novel implementation of sediment handling is presented where both averaged and separate values for sediment species are used to ensure speed and precision in the simulations.

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 purpose of this paper is to investigate numerically thermal convection heat transfer in closed square and cubical cavities with local energy sources of various geometric shapes.

The analyzed regions are square and cubical cavities with two isothermally cold opposite vertical walls, whereas other walls are adiabatic. A local energy element of rectangular, trapezoidal or triangular shape is placed on the lower surface of the cabinet. The lattice Boltzmann technique has been used as the main method for the problem solution in two-dimensional (2D) and three-dimensional (3D) formulations, whereas the finite difference technique with non-primitive parameters such as stream function and vorticity has been also used.

The velocity and temperature fields for a huge range of Rayleigh number 104–106, as well as for various geometry shapes of the heater have been studied. A comparative analysis of the results obtained on the basis of two numerical techniques for 2D and 3D formulations has been performed. The dependences of the energy transfer strength in the region on the shape of energy source and Rayleigh number have been established. It has been revealed that the triangular shape of the energy source corresponds to the maximum values of the velocity vector and temperature within the cavity, and the rectangular shape corresponds to the minimum values of these mentioned variables. With the growth of the Rayleigh number, the difference in the values of these mentioned variables for rectangular and triangular shapes of heaters also increases.

The originality of this work is to scrutinize the lattice Boltzmann method and finite difference method for the problem of natural convection in 2D and 3D closed chambers with a local heated element.

The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task.

The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods.

The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems.

The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two‐dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two‐dimensional dam‐break problem and the approximate solution compares well with those given by other authors.

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.

In computational fluid dynamics for two-phase reactive flow of interior ballistic, the conventional schemes (MacCormack method, etc.) are known to introduce unphysical oscillations in the region where the gradient is high. This paper aims to improve the ability to capture the complex shock wave during the interior ballistic cycle.

A two-phase flow model is established to describe the complex physical process based on a modified two-fluid theory. The solution of model is obtained including the following key methods: an approximate Riemann solver to construct upwind fluxes, the MUSCL extension to achieve high-order accuracy, a splitting approach to solve source terms, a self-adapting method to expand the computational domain for projectile motion and a control volume conservation method for the moving boundary.

The paper is devoted to applying a high-resolution numerical method to simulate a transient two-phase reactive flow with moving boundary in guns. Several verification tests demonstrate the accuracy and reliability of this approach. Simulation of two-phase reaction flow with a projectile motion in a large-caliber gun shows an excellent agreement between numerical simulation and experimental measurements.

This paper has implications for improving the ability to capture the complex physics phenomena of two-phase flow during interior ballistic cycle and predict the combustion details, such as the flame spreading, the formation of pressure waves and so on.

This approach is reliable as a prediction tool for the understanding of the physical phenomenon and can therefore be used as an assessment tool for future interior ballistics studies.

The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.

The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.

The method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.

While relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.

The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.

The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.

Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.

The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.

The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.