Pressure Stabilization Method Research Articles

Pressure stabilization method for the 2D/3D time‐dependent natural convection equations with salt concentration

AbstractIn this paper, the pressure stabilization method for the 2D/3D time‐dependent natural convection equations with salt concentration (NCSC) is considered. The artificial pressure diffusion term is introduced to reduce the constraint of the incompressible condition. The first‐order backward difference formula is adopted to approximate the temporal derivative terms, the diffusion terms in NCSC are treated implicitly, the convective terms in momentum equation are treated semi‐implicitly, the convective terms in energy equation and salt concentration equation are treated implicitly. The error estimates for the semi‐discrete pressure stabilization method are given. Some numerical experiments are presented to verify the theoretical results and show the reliability of the proposed method.

Blowing pressure stabilization method for the artificial excitation of reed instruments (L).

To investigate the acoustics of reed instruments without the need for a human player, blowing machines are needed, which can generate air pressures up to 8 kPa and flow rates up to 40 liters per minute. Due to reed flexibility and the changing pressure gradient across the reed, the relationship between flow and pressure is highly non-linear. Since the output pressure of ventilators is highly dependent on flow, non-linear pressure regulation is a difficult task that requires a closed-loop approach. Since reed vibration starts suddenly when blowing pressure is gradually increased, an abrupt change in airflow through the instrument is present, resulting in a change in pressure in the artificial mouth. To avoid that, a method is presented to achieve a fast response to abrupt flow changes, which is tested in an existing blowing machine. The enhanced blowing machine exhibits a settling time below 200 ms, which allows for the generation of blowing pressures with linear responses.

Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method

Existence of Weak Solution to the Nonstationary Navier-Stokes Equations Approximated by Pressure Stabilization Method

Estimation of the reliability of determination of filtering parameters of productive formations using multi-dimensional regression analysis

Determination of reliable values of filtration parameters of productive strata is the most important task of monitoring the processes of developing reserves. One of the most effective methods for solving the problem is hydrodynamic testing of wells using the pressure recovery method, as well as modern methods - the pressure stabilization method and the method based on production analysis (Decline Analyze). This article is devoted to the assessment of the reliability of these three methods in determining the filtration parameters of terrigenous and carbonate productive deposits of oil fields in the Perm Krai. To solve the problem, multivariate regression analysis was used. A series of multidimensional mathematical models of well flow rates was built using filtration parameters determined for each of the methods. It is proposed to consider the filtration parameters included in the models with the maximum statistical estimates of performance as the most reliable. With regard to the fields under consideration, it was found that in terrigenous reservoirs, all three methods demonstrate stable results. In carbonate reservoirs, reliable values of filtration parameters are determined by processing pressure build-up curves. Pressure stabilization and production analysis methods show less robust results and require additional research in order to develop sound recommendations for their practical application. Keywords: permeability; skin factor; pressure stabilization curve; decline analyze; liquid flow rate; geological and technological parameters; oil deposit; carbonate deposits.

Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities

In this study, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model comprises a Cahn–Hilliard equation, Navier–Stokes equation, and the generalized Navier boundary condition for the moving contact line. A scalar auxiliary variable is employed to transform the governing system into an equivalent form, thereby allowing the double well potential to be treated semi-explicitly. A stabilization term is added to balance the explicit nonlinear term originating from the surface energy at the fluid–solid interface. A pressure stabilization method is used to decouple the velocity and pressure computations. Some subtle implicit–explicit treatments are employed to deal with convention and stress terms. We establish a rigorous proof of the energy stability for the proposed time-marching scheme. A finite difference method based on staggered grids is then used to spatially discretize the constructed time-marching scheme. We also prove that the fully discrete scheme satisfies the discrete energy dissipation law. Our numerical results demonstrate the accuracy and energy stability of the proposed scheme. Using our numerical scheme, we analyze the contact line dynamics based on a shear flow-driven droplet sliding case. Three-dimensional droplet spreading is also investigated based on a chemically patterned surface. Our numerical simulation accurately predicts the expected energy evolution and it successfully reproduces the expected phenomena where an oil droplet contracts inward on a hydrophobic zone and then spreads outward rapidly on a hydrophilic zone.

A mixed upwind/central WENO scheme for incompressible two-phase flows

In this paper, an accurate and efficient numerical scheme is developed to solve the Navier-Stokes equations for two-phase flow systems with the nonlinear inertial term in conservation form. The major difficulty of discretizing the nonlinear inertial term in conservation form in two-phase flows is rooted in the discontinuous nature of momentum across interfaces. To overcome this difficulty, we developed the mixed Upwind/Central WENO scheme so that no grid deformation or mapping, or explicit interface reconstruction is necessary. Our mixed Upwind/Central WENO scheme also removes the dependence on the interface tracking/capturing method so it is compatible with any popular interface tracking/capturing methods. To decouple the overall equations of the two-phase system, an efficient semi-implicit projection scheme is constructed, which shares the efficiency of pressure stabilization method while enforces divergence-free condition to machine precision, to benefit interface advection, reduction consistency as well as large density ratio. The accuracy and reduction consistency of this projection scheme are validated by numerical experiments. Several benchmark cases are performed to show the capability of the overall scheme handling realistic two-phase problems with multiple physical effects, complex interface evolution and/or large density ratio of the order of (ρwater/ρair). Both quantitative and qualitative comparisons have been made and very good agreements with analytical solutions, published numerical and/or experimental results are achieved.

On pressure stabilization method for nonstationary Navier-Stokes equations

In this paper, we consider the nonstationary Navier-Stokes equations approximated by the pressure stabilization method. We can obtain the local in time existence theorem for the approximated Navier-Stokes equations. Moreover we can obtain the error estimate between the solution to the usual Navier-Stokes equations and the Navier-Stokes equations approximated by the pressure stabilization method.

Approximation of the unsteady Brinkman‐Forchheimer equations by the pressure stabilization method

In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman‐Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second‐order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1949–1965, 2017

A two-level pressure stabilization method for the generalized Stokes problem

Stabilization mixed methods that circumvent the restrictive inf–sup condition without introducing penalty errors have been developed for Stokes equations e.g. by Franca, Hughes and Stenberg in 1993, and Bonvin, Picasso and Stenberg in 2001. These methods consist of modifying the standard Galerkin formulation by adding mesh-dependent terms, which are weighted residuals of the original differential equations. The aim of the stabilization, however, is to select minimal terms that stabilize the approximation without losing the nice conservation properties. Although for properly chosen stabilization parameters these methods are well posed for all velocity–pressure pairs, numerical results reported by several researchers seem to indicate that these methods are sensitive to the choice of the stabilization parameters. A relatively recent stabilized finite-element formulation that seeems less sensitive to the choice of parameters and has better local conservation properties was developed and analysed by Codina and Blasco in 1997, Becker and Braack in 2001, and Nafa in 2004. This method consists of introducing the L2-projection of the pressure gradient as a new unknown of the problem. Hence, a third equation to enforce the projection property is added to the original discrete equations, and a weighted difference of the pressure gradient and its projection are introduced into the continuity equation. In this paper, as done by Nafa in 2006, we analyse the pressure gradient stabilization method for the generalized Stokes problem and investigate its stability and convergence properties.

Simulation of natural convection with the collocated clustered finite volume scheme

This paper presents numerical results obtained in the case of natural convection within non constant fluid density, using the collocated clustered finite volume (CCFV) scheme. The continuous equations are first given in a dimensionless form. Then we present the finite volume scheme with the principles and the spatial discretization used. Analytical tests illustrate the numerical behavior of this scheme according to the type of grid, of the pressure stabilization method and check the robustness of this scheme. Next, the results obtained on the square thermally driven cavity under large temperature differences show that the CCFV scheme accurately fits the reference results.

A simple pressure stabilization method for the Stokes equation

AbstractIn this paper, we consider a stabilization method for the Stokes problem, using equal‐order interpolation of the pressure and velocity, which avoids the use of the mesh size parameter in the stabilization term. We show that our approach is stable for equal‐order interpolation in the case of piecewise linear and piecewise quadratic polynomials on triangles. In the case of linear polynomials, we retrieve a well‐known idea of using mass lumping as a stabilization mechanism. Copyright © 2007 John Wiley & Sons, Ltd.

Pressure Stabilization Method for Steady Viscous Flows in a System of Pipes

This paper deals with a singular perturbation of the stationary Stokes and Navier-Stokes systems. The term e2Δp is added to the continuity equation, where e is a small parameter. For a domain with cylindrical outlets to infinity and exponentially decaying data, existence and uniqueness of solutions under flux conditions at infinity are established for the linear problem and also for the nonlinear problem in the case of small data. Asymptotically exact estimates are proved for e tending to zero. For sufficiently regular data, these estimates imply the convergence in H loc 5/2−δ for the velocity parts and in H loc 3/2−δ for the pressure parts, respectively. Bibliography: 17 titles.

Linear elements for metal-forming problems within the flow approach

Simulation of transient and stationary metal-forming processes is presented in the context of a mixed velocity–pressure formulation with a rigid-viscoplastic material model. A fractional step technique is used to obtain in a natural way a discrete Laplacian in the pressure–pressure entries of the system matrix which, as is known, introduces the stabilizing effect and allows for the use of equal order interpolating functions for both discretized variables, in spite of the Babuska–Brezzi condition. The method is suitable for both implicit and explicit time integration schemes. In particular, the explicit version (forward Euler with mass lumping) is developed. The discretization is carried out for linear triangles and tetrahedra which most easily can make use of automatic mesh generators and result in a simple code. Attention is focused on the stabilizing effect as a function of material and numerical parameters. The technique is illustrated with extrusion and upsetting simulation and compared with a known pressure stabilization method.