Zonal disturbance region update method for steady compressible viscous flows

A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

In this contribution, we use an adaptive unstructured grid algorithm for the solution of steady laminar compressible viscous flows over compression corners. The spatial discretisation is achieved by means of general assemblies of triangular or quadrilateral cells, while the temporal discretisation is accomplished in a fully implicit fashion. The unknowns are associated with the cell vertices [1,2] and a first order upwind algorithm results from the use of the flux difference splitting method of Roe [3]. A higher order extension is achieved by using the MUSCL concepts of van Leer [4]. This requires a monotonic linear reconstruction of the solution on a general unstructured grid and this is accomplished by the use of variational recovery [5] with the incorporation of the slope limiting [6]. The solution of the implicit equation system is obtained by a point implicit relaxation process.

Disturbance region update method with preconditioning for steady compressible and incompressible flows

Numerical modelling of compressible flows around moving solids is important for engineering applications such as aerodynamic flutter, rocket engines and landing gear. The penalty function method is particularly effective when using orthogonal structural meshes within a finite difference scheme and is widely used to solve both laminar and turbulent flow problems. The method is based on the direct application of the Navier-Stokes equations with added sources, which allows the boundary conditions to be set indirectly. This method facilitates the imposition of Dirichlet boundary conditions but complicates the application of Neumann conditions. Nevertheless, the method works well with both types of boundary conditions, making it suitable for thermal and compressible flows where Neumann conditions are often used. Despite its flexibility, the method requires a high degree of data management and additional coding. This paper presents results of a recently developed higher-order method for compressible subsonic flows, demonstrating accurate modeling of moving objects without numerical noise. The method has been tested on stationary and moving objects over a wide range of Reynolds and Mach numbers.

Enhanced anisotropic block-based adaptive mesh refinement for three-dimensional inviscid and viscous compressible flows

A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows

A pressure‐based semi‐implicit procedure has been developed for the computation of compressible flows on a system with collocated finite volume formulations. The method includes the implementation of a high‐order accurate weighted essentially non‐oscillatory scheme within the pressure‐based algorithm which employs an approximate Riemann solver for the computation of the cell face inviscid fluxes. The developed scheme is applied to the computation of unsteady compressible flow through a shock tube which experiences various Mach numbers, and the computations are compared with an analytical solution. The computations indicate that the developed procedure leads to sharp discontinuity representation without creation of spurious oscillations. Then, the developed numerical method is utilized to investigate unsteady two‐dimensional flow for a lax configuration and the results are compared with the results of the similar scheme in the density‐based algorithm. At the end, the investigation of steady compressible flows in bump and wedge channel is considered. The simulations show a considerable improvement over the existing pressure‐based method. The investigations show that the developed method is suitable for studying compressible steady and unsteady flows.

A new partial upwind finite element method for steady viscous incompressible flow over a wide range of Reynolds numbers (Re) is proposed and its applications to a cavity flow problem are demonstrated. Numerical experiments show that the partial upwind scheme is effective for Re = 103 when the conventional Galerkin type approximation produces poor results. The partial upwind scheme for the finite element method was originally developed by Ikeda (1983) for approximation of the advection diffusion equation. The advantage of the scheme is its effectiveness over a wide range of Peclet numbers due to the automatic switch in the approximation techniques of the advection term.

Hypersonic similarity for steady compressible full Euler flows over two-dimensional Lipschitz wedges

The paper presents the asymptotic solution, near a stationary contact line at a plane boundary, for steady viscous incompressible flow of two immiscible liquids. The eigenvalues which determine this Stokes flow are determined by the contact angle α of the more viscous liquid and the ratio μ of the two viscosities. The dominant eigenvalues are found for all values of α and μ. As μ → 0 the results agree with those of Moffatt's (1964) one-phase theory for the case μ = 0 only when α > 81°. For α < 81° the two sets of results are qualitatively different. In particular, the eddy structure corresponding to complex eigenvalues occurs only in the α-range (34°, 81°). As μ increases from 0 to 1, this range steadily decreases to zero, which is located at 60°. The transport of energy across the liquid interface is almost always from the obtuse-angled sector to the acute-angled sector, irrespective of α, μ, and the location of the global power supply.

An investigation of laminar steady and unsteady flows in a two‐dimensional T‐junction was carried out for Newtonian and a non‐Newtonian fluid analogue to blood. The flow conditions considered are of relevance to hemodynamical applications and the localization of coronary diseases, and the main objective was to quantify the accuracy of the predictions and to provide benchmark data that are missing for this prototypical geometry. Under steady flow, calculations were performed for a wide range of Reynolds numbers and extraction flow rate ratios, and accurate data for the recirculation sizes were obtained and are tabulated. The two recirculation zones increased with Reynolds number, but the behaviour was non‐monotonic with the flow rate ratio. For the pulsating flows a periodic instability was found, which manifests itself by the breakdown of the main vortex into two pieces and the subsequent advection of one of them, while the secondary vortex in the main duct was absent for a sixth of the oscillating period. Shear stress maxima were found on the walls opposite the recirculations, where the main fluid streams impinge onto the walls. For the blood analogue fluid, the recirculations were found to be 10% longer but also short lived than the corresponding Newtonian eddies, and the wall shear stresses are also significantly different especially in the branch duct. Copyright © 2007 John Wiley & Sons, Ltd.

Three-dimensional steady and unsteady (pulsating) compressible flows in a vane-less turbocharger turbine of a 1.7 liter SI engine are simulated numerically, and the results are validated experimentally using a turbocharged on-engine test cell. Simulations are carried out for a 720° engine cycle at three engine speeds, and the complete forms of volute and rotor vanes are modeled. Two ways for modeling the rotating wheel, multiple reference frames (MRF), and sliding mesh (SM) techniques are also examined. Finally, the effects of pulsating flow on the turbocharger turbine performance parameters (TTPP) such as the inlet static pressure, reduced mass flow rate, and efficiency are obtained and compared with their values under steady flow. The results show that the accuracy of steady characteristic map to estimate the TTPPs has some source of ambiguity, which should be considered for detailed analysis. TTPP values under steady flow conditions are found to be significantly deviated from the unsteady results. These deviations are decreased as the engine speed increases.

A new Cartesian grid system approach is proposed for the numerical simulation of two-dimensional compressible viscous flows around an arbitrary shape body. The grid system is constructed of patched blocks which is composed of the nested-spacing regular grid. The numerical procedure is based on the method of lines. For the spatial discretization, the neighboring-point local collocation method is developed and introduced for the grid points near the body, and the 2nd-order central difference method is used for the points far from the body. The 2-stage Runge-Kutta method (RK 2) is used for the time integration scheme. For the unsteady solution the nesting time step technique is combined with RK 2. Numerical results are obtained for subsonic steady and unsteady flows around a circular cylinder and compared with the other results. The results for transonic and supersonic steady flows over NACA 0012 are compared with the GAMM workshop ones. The present approach is confirmed to be applicable for the arbitrary shape body, and the computational cost is about 50% that of the conventional boundary-fitted grid approach.

A study for the effect of non-uniform slot injection/suction and non-uniform total enthalpy at the wall for a steady non-similar laminar compressible boundary layer flow over a rotating sphere is presented. The effects of rotation and free stream Mach number have also been considered. Non-similar solutions have been obtained from the starting point of the stream wise coordinate to the point of separation using an implicit finite difference scheme in combination with the quasi-linearization technique. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the non-uniform slot injection has just the opposite effect. An increase of rotation and total enthalpy at the wall causes separation to occur earlier while cooling delays it. An increase of the Mach number shifts the point of separation upstream due to the adverse pressure gradient. The non-uniform total enthalpy at the wall has a very little effect on the skin friction and hence on the point of separation.

Compressibility transformations have received considerable attention for extending well-established incompressible wall models to high-speed flows. While encouraging progress has been made in mean velocity scalings, research on temperature transformations has lagged behind. In this study, we rigorously derive a general framework for both velocity and temperature transformations directly from the compressible Reynolds-averaged Navier–Stokes (RANS) equations and their ‘incompressible’ counterparts, elucidating how these transformations guide the development of compressible algebraic RANS models in the inner layer. The introduction of the mixed Prandtl number further links the mean momentum and energy transport, facilitating the formulation of novel temperature transformations through integration with arbitrary mean velocity scalings, thereby unifying existing transformation methods while providing a systematic approach for further improvement. A detailed evaluation using direct numerical simulation databases of canonical compressible wall-bounded turbulent flows (CWBTFs) demonstrates that temperature transformations based on the Griffin–Fu–Moin and our recently proposed velocity scalings exhibit superior accuracy and robustness across a wide range of Reynolds and Mach numbers, as well as varying wall thermal boundary conditions. We also perform a preliminary investigation into the applicability of the proposed integral mean temperature–velocity relation and inverse temperature transformations for near-wall temperature modelling in cold-wall boundary layer flows, where discontinuities caused by non-monotonic temperature distributions are effectively avoided. Although the omission of higher-order terms in deriving the total heat flux equation enables closed-form wall modelling, it remains a key limitation to the model’s accuracy at the current stage. Future work may therefore need to address this issue to achieve further advances. These findings enhance the physical understanding of mean momentum and energy transport in canonical CWBTFs, and offer promising prospects for advancing near-wall temperature modelling within RANS and wall-modelled large eddy simulation frameworks.