The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Jeanclaude Latche - One of the best experts on this subject based on the ideXlab platform.
-
an unconditionally stable staggered Pressure Correction scheme for the compressible navier stokes equations
The SMAI journal of computational mathematics, 2016Co-Authors: Dionysios Grapsas, Raphaele Herbi, Walid Kheriji, Jeanclaude LatcheAbstract:In this paper we present a Pressure Correction scheme for the compressible Navier-Stokes equations. The space discretization is staggered, using either the Marker-And Cell (MAC) scheme for structured grids, or a nonconforming low-order finite element approximation for general quandrangular, hexahedral or simplicial meshes. For the energy balance equation, the scheme uses a discrete form of the conservation of the internal energy, which ensures that this latter variable remains positive; this relation includes a numerical corrective term, to allow the scheme to compute correct shock solution in the Euler limit. The scheme is shown to have at least one solution, and to preserve the stability properties of the continuous problem, irrespectively of the space and time steps. In addition, it naturally boils down to a usual projection scheme in the limit of vanishing Mach numbers. Numerical tests confirm its potentialities, both in the viscous incompressible and Euler limits.
-
an unconditionally stable Pressure Correction scheme for the compressible barotropic navier stokes equations
Mathematical Modelling and Numerical Analysis, 2008Co-Authors: Thierry Galloue, Laura Gastaldo, Raphaele Herbi, Jeanclaude LatcheAbstract:We present in this paper a Pressure Correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based ap rioriestimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretiza- tions, both interesting for their own sake: the L 2 -stability of the discrete advection operator provided it is consistent, in some sense, with the mass balance and the estimate of the Pressure work by means of the time derivative of the elastic potential. The proposed scheme is built in order to match these theoretical results, and combines a fractional-step time discretization of Pressure-Correction type with a space discretization associating low order non-conforming mixed finite elements and finite volumes. Numerical tests with an exact smooth solution show the convergence of the scheme.
Antonino Ferrante - One of the best experts on this subject based on the ideXlab platform.
-
a fast Pressure Correction method for incompressible flows over curved walls
Journal of Computational Physics, 2020Co-Authors: Abhiram Aithal, Antonino FerranteAbstract:Abstract We have developed an explicit and direct Pressure-Correction method for simulating incompressible flows over curved walls. In order to integrate the Navier Stokes (NS) equations in time, we have developed an explicit, three-stage, third-order Runge-Kutta based projection-method (FastRK3) which requires solving the Poisson equation for Pressure only once per time step. We have chosen to discretize the incompressible NS equations written in the orthogonal coordinates rather than the general formulation in curvilinear coordinates because the former does not contain cross-derivatives in the advection, diffusion, Laplacian, and gradient operators. Thus, the computational cost of solving the NS equations is substantially reduced and the numerical stencils of the finite difference approximations to these operators mirror that of the Cartesian formulation. This property also allows us to develop an FFT-based Poisson solver for Pressure (FastPoc) for those cases where the components of the metric tensor are independent of one spatial direction: surfaces of linear translation (e.g., curved ramps and bumps) and surfaces of revolution (e.g., axisymmetric ramps). We have verified and validated FastRK3 and we have applied FastRK3 for simulating separated flows over ramps and a bump. Finally, our results show that the new FFT-based Poisson solver, FastPoc, is thirty to sixty times faster than the multigrid-based linear solver (depending on the tolerance set for the multigrid solver), and the new flow solver, FastRK3, is overall four to seven times faster when using FastPoc rather than multigrid. In summary, given that the computational mesh satisfies the property of orthogonality, FastRK3 can simulate flows over curved walls with second-order accuracy in space.
-
a fast Pressure Correction method for incompressible two fluid flows
Journal of Computational Physics, 2014Co-Authors: Michael Dodd, Antonino FerranteAbstract:We have developed a new Pressure-Correction method for simulating incompressible two-fluid flows with large density and viscosity ratios. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier-Stokes equations for two-fluid flows is reduced to a constant coefficient equation, which can be solved with an FFT-based, fast Poisson solver. This reduction is achieved by splitting the variable density Pressure gradient term in the governing equations. The validity of this splitting is demonstrated from our numerical tests, and it is explained from a physical viewpoint. In this paper, the new Pressure-Correction method is coupled with a mass-conserving volume-of-fluid method to capture the motion of the interface between the two fluids but, in general, it could be coupled with other interface advection methods such as level-set, phase-field, or front-tracking. First, we verified the new Pressure-Correction method using the capillary wave test-case up to density and viscosity ratios of 10,000. Then, we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value. Next, the method is shown to be second-order accurate in space and time independent of the VoF method, and it conserves mass, momentum, and kinetic energy in the inviscid limit. Also, we show that for solving the two-fluid Navier-Stokes equations, the method is 10-40 times faster than the standard Pressure-Correction method, which uses multigrid to solve the variable coefficient Poisson equation. Finally, we show that the method is capable of performing fully-resolved direct numerical simulation (DNS) of droplet-laden isotropic turbulence with thousands of droplets using a computational mesh of 1024^3 points.
Erik Dick - One of the best experts on this subject based on the ideXlab platform.
-
a combined momentum interpolation and advection upstream splitting Pressure Correction algorithm for simulation of convective and acoustic transport at all levels of mach number
Published by Elsevier BV, 2019Co-Authors: Yann Moguen, Pascal Bruel, Erik DickAbstract:A Pressure-Correction algorithm is presented for compressible fluid flow regimes. It is well-suited to simulate flows at all levels of Mach number with smooth and discontinuous flow field changes, by providing a precise representation of convective transport and acoustic propagation. The co-located finite volume space discretization is used with the AUSM flux splitting. It is demonstrated that two ingredients are essential for obtaining good quality solutions: the presence of an inertia term in the face velocity expression; a velocity difference diffusive term in the face Pressure expression, with a correct Mach number scaling to recover the hydrodynamic and acoustic low Mach number limits. To meet these two requirements, a new flux scheme, named MIAU, for Momentum Interpolation with Advection Upstream splitting is proposed.
-
mach uniformity through the coupled Pressure and temperature Correction algorithm
Journal of Computational Physics, 2005Co-Authors: Krista Nerinck, Ja Vierendeels, Erik DickAbstract:We present a new type of algorithm: the coupled Pressure and temperature Correction algorithm. It is situated in between the fully coupled and the fully segregated approach, and is constructed such that Mach-uniform accuracy and efficiency are obtained. The essential idea is the separation of the convective and the acoustic/thermodynamic phenomena: a convective predictor is followed by an acoustic/thermodynamic corrector. For a general case, the corrector consists of a coupled solution of the energy and the continuity equations for both Pressure and temperature Corrections. For the special case of an adiabatic perfect gas flow, the algorithm reduces to a fully segregated method, with a Pressure-Correction equation based on the energy equation. Various test cases are considered, which confirm that Mach-uniformity is obtained.
Daniele Antonio Di Pietro - One of the best experts on this subject based on the ideXlab platform.
-
a Pressure Correction scheme for convection dominated incompressible flows with discontinuous velocity and continuous Pressure
Journal of Computational Physics, 2011Co-Authors: Lorenzo Alessio Otti, Daniele Antonio Di PietroAbstract:In this work we present a Pressure-Correction scheme for the incompressible Navier-Stokes equations combining a discontinuous Galerkin approximation for the velocity and a standard continuous Galerkin approximation for the Pressure. The main interest of Pressure-Correction algorithms is the reduced computational cost compared to monolithic strategies. In this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high Reynolds regimes. The proposed spatial velocity-Pressure approximation is LBB stable for equal polynomial orders and it allows adaptive p-refinement for velocity and global p-refinement for Pressure. The method is validated against a large set of classical two- and three-dimensional test cases covering a wide range of Reynolds numbers, in which it proves effective both in terms of accuracy and computational cost.
Jie She - One of the best experts on this subject based on the ideXlab platform.
-
a Pressure Correction scheme for generalized form of energy stable open boundary conditions for incompressible flows
Journal of Computational Physics, 2015Co-Authors: Suchua Dong, Jie SheAbstract:We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary conditions, which all ensure the energy stability of the system, even in situations where strong vortices or backflows occur at the open/outflow boundaries. Our numerical algorithm for treating these open boundary conditions is based on a rotational Pressure Correction-type strategy, with a formulation suitable for C 0 spectral-element spatial discretizations. We have introduced a discrete equation and associated boundary conditions for an auxiliary variable. The algorithm contains constructions that prevent a numerical locking at the open/outflow boundary. In addition, we have developed a scheme with a provable unconditional stability for a sub-class of the open boundary conditions. Extensive numerical experiments have been presented to demonstrate the performance of our method for several flow problems involving open/outflow boundaries. We compare simulation results with the experimental data to demonstrate the accuracy of our algorithm. Long-time simulations have been performed for a range of Reynolds numbers at which strong vortices or backflows occur at the open/outflow boundaries. We show that the open boundary conditions and the numerical algorithm developed herein produce stable simulations in such situations.
-
error analysis of Pressure Correction schemes for the time dependent stokes equations with open boundary conditions
SIAM Journal on Numerical Analysis, 2005Co-Authors: Jeanluc Guermond, Pete D Minev, Jie SheAbstract:The incompressible Stokes equations with prescribed normal stress (open) boundary conditions on part of the boundary are considered. It is shown that the standard Pressure-Correction method is not suitable for approximating the Stokes equations with open boundary conditions, whereas the rotational Pressure-Correction method yields reasonably good error estimates. These results appear to be the first ever published for splitting schemes with open boundary conditions. Numerical results in agreement with the error estimates are presented.
-
on the error estimates for the rotational Pressure Correction projection methods
Mathematics of Computation, 2003Co-Authors: Jeanluc Guermond, Jie SheAbstract:In this paper we study the rotational form of the Pressure-Correction method that was proposed by Timmermans, Minev, and Van De Vosse. We show that the rotational form of the algorithm provides better accuracy in terms of the H1-norm of the velocity and of the L2-norm of the Pressure than the standard form.
