scholarly journals Hybrid Flux Method in Monotonicity-Preserving Scheme for Accurate and Robust Simulation in Supersonic Flow

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Myeong-Hwan Ahn ◽  
Duck-Joo Lee
Keyword(s):  
Blow Up ◽  
Supersonic Jet ◽  
Positive Density ◽  
Computational Domain ◽  
Flux Method ◽  
Present Scheme ◽  
Local Extrema ◽  
Volume Method ◽  
Fifth Order ◽  
Monotonicity Preserving

The fifth-order monotonicity-preserving (MP5) scheme is an accurate and low dissipative numerical method. As a finite-volume method, MP5 adopts the Roe-flux scheme for solving the numerical flux in the compressible Euler equation. However, due to the deficiency of the MP limiter and Roe-flux in maintaining positive density and pressure, the calculation could fail in cases of extreme flow involving small values of density and pressure. In this study, to overcome such a limitation but still to achieve a high-accuracy of MP5, we propose a hybrid flux method: the Roe-flux is used in the global computational domain, but the first-order Lax-Friedrich (LF)-flux is adopted only for trouble grids. The numerical results of shock-tube and complicated interaction problems indicate that the present scheme is more accurate at discontinuities and local extrema compared to the previous scheme, maintaining positive density and pressure values. For two-dimensional applications, a supersonic jet is explored with different Mach numbers and temperature conditions. As a result, small vortices induced by the shear layer can be clearly captured by the proposed scheme. Furthermore, a simulation was successfully conducted without blow-up of calculation even in the extreme jet flow condition.

An Improved Hybrid Alternative WENO Scheme for High Mach Number Flows

2021 ◽  
Author(s):  
Uttam Singh Rajput ◽  
Krishna Mohan Singh
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Weno Scheme ◽  
Test Cases ◽  
Present Scheme ◽  
Low Dissipation ◽  
Scale Structures ◽  
High Mach ◽  
Fifth Order ◽  
High Resolution Method

Abstract This study presents the development of a fifth-order hybrid alternative mapped weighted essentially non-oscillatory scheme (HAW-M) for high-speed compressible flows. A new, improved smoothness indicator has been developed to design the HAW-M scheme. The performance of the present scheme has been evaluated through different one and two-dimensional test cases. The developed scheme shows higher accuracy and low dissipation. Further, it captures the fine-scale structures smoothly than the existing high-resolution method.

scholarly journals Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography

2020 ◽  
Vol 50 (3) ◽  
pp. 287-302
Author(s):  
Róbert ČUNDERLÍK ◽  
Matej MEDĽA ◽  
Karol MIKULA
Keyword(s):  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Scale ◽  
Horizontal Resolution ◽  
Geopotential Model ◽  
Computational Domain ◽  
Disturbing Potential ◽  
Volume Method ◽  
Upper Boundary

The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

Simulation of Turbulent Flows Using a Finite-Volume Based Lattice Boltzmann Flow Solver

2014 ◽  
Vol 17 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Goktan Guzel ◽  
Ilteris Koc
Keyword(s):  
Fluid Flow ◽  
Turbulent Flows ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Computational Effort ◽  
Computational Domain ◽  
Flow Solver ◽  
Turbulent Fluid Flow ◽  
Finite Volume Approach ◽  
Volume Method

AbstractIn this study, the Lattice Boltzmann Method (LBM) is implemented through a finite-volume approach to perform 2-D, incompressible, and turbulent fluid flow analyses on structured grids. Even though the approach followed in this study necessitates more computational effort compared to the standard LBM (the so called stream and collide scheme), using the finite-volume method, the known limitations of the stream and collide scheme on lattice to be uniform and Courant-Friedrichs-Lewy (CFL) number to be one are removed. Moreover, the curved boundaries in the computational domain are handled more accurately with less effort. These improvements pave the way for the possibility of solving fluid flow problems with the LBM using coarser grids that are refined only where it is necessary and the boundary layers might be resolved better.

Natural Convection in Vertical Channels with Porous Media and Adiabatic Extensions

2010 ◽  
Vol 297-301 ◽  
pp. 1432-1438
Author(s):  
Assunta Andreozzi ◽  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini
Keyword(s):  
Natural Convection ◽  
Wall Temperature ◽  
Finite Extension ◽  
Darcy Number ◽  
Geometrical Parameters ◽  
Computational Domain ◽  
Stream Condition ◽  
Diffusive Effects ◽  
Volume Method ◽  
Heated Plates

A numerical investigation on natural convection in air in a vertical heated channel, partially filled with porous medium, with adiabatic extensions downward and collinear the heated plates is accomplished. The fluid flow is assumed two-dimensional, laminar, steady state and incompressible. The porous material is considered as homogeneous and isotropic and the Brinkman-Forchheimer-extended Darcy model is considered. A finite-extension computational domain is employed to simulate the free-stream condition and allows to account for the diffusive effects and the numerical results are obtained using the finite volume method by FLUENT. Results in terms of wall temperature profiles are presented to evaluate the effects of the main thermal and geometrical parameters. The adiabatic extensions determine a wall temperature decrease and wall temperature decreases increasing Darcy number. In full filled heated channels wall temperature presents a significant increase for Darcy number decrease.

An Unstructured Reacting Flow Solver With Coupled Implicit Solution of the Species Conservation Equations

2008 ◽  
Author(s):  
Ankan Kumar ◽  
Sandip Mazumder
Keyword(s):  
Species Conservation ◽  
Domain Size ◽  
Reacting Flow ◽  
Computational Domain ◽  
Conservation Equations ◽  
Flow Solver ◽  
As Species ◽  
Minimum Residual ◽  
Volume Method ◽  
Coupled Solution

Many reacting flow applications mandate coupled solution of the species conservation equations. A low-memory coupled solver was developed to solve the species transport equations on an unstructured mesh with implicit spatial as well as species-to-species coupling. First, the computational domain was decomposed into sub-domains comprised of geometrically contiguous cells—a process termed internal domain decomposition (IDD). This was done using the binary spatial partitioning (BSP) algorithm. Following this step, for each sub-domain, the discretized equations were developed using the finite-volume method, written in block implicit form, and solved using an iterative solver based on Krylov sub-space iterations, i.e., the Generalized Minimum Residual (GMRES) solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain interfaces and non-linearities in the governing equations. The solver is demonstrated for a laminar ethane-air flame calculation with five species and a single reaction step, and for a catalytic methane-air combustion case with 19 species and 22 reaction steps. It was found that the best performance is manifested for sub-domain size of about 1000 cells, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2–5 over the block Gauss-Seidel procedure.

Front Tracking Approach and Application to Multi-Fluid Flow

2006 ◽  
Author(s):  
Manasa Ranjan Behera ◽  
K. Murali
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Fixed Grid ◽  
Moving Interface ◽  
Fluid Properties ◽  
Volume Method ◽  
Transfer Of Information

Multiphase flows simulations using a robust interface-tracking method, are presented. The method is based on writing one set of governing equations for the whole computational domain and treating the different phases as single fluid domain with variable material properties. Interfacial terms are accounted for by adding the appropriate sources as δ functions at the boundary separating the phases. The unsteady Navier-Stokes equations are solved by finite volume method on a fixed, structured grid and the interface, or front, is tracked explicitly by a lower dimensional grid. Interfacial source terms are computed on the front and transferred to the fixed grid. Advection of fluid properties such as density and viscosity is done by following the motion of the front. The method has been implemented for interfacial flow problems, depicting the interface and topology change capturing capability. The representation of the moving interface and its dynamic restructuring, as well as the transfer of information between the moving front and the fixed grid, is discussed. Extensions of the method to density stratified flows, and interfacial movements are then presented.

Assessment of Enhanced Multi-Dimensional Limiting Process for Multi-Dimensional Flows

2011 ◽  
Author(s):  
Kyu Hong Kim ◽  
Jung Ho Park
Keyword(s):  
Higher Order ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Interpolation Scheme ◽  
Local Extrema ◽  
Numerous Test ◽  
High Order Interpolation

In this paper, a new limiting process based on the Multi-dimensional Limiting Process, called enhanced Multi-dimensional Limiting Process is developed and tested with several cases. The enhanced Multi-dimensional Limiting Process, e-MLP has a number of useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. The new limiting process was applied to numerous test cases. Through these tests, we could confirm that e-MLP enhances the accuracy and efficiency with both continuous and discontinuous multidimensional flows.

Numerical Analysis of General Groove Geometry for Dry Gas Seals

2013 ◽  
Vol 457-458 ◽  
pp. 544-551
Author(s):  
Ji Bin Hu ◽  
Wen Jin Tao ◽  
Yi Min Zhao ◽  
Chao Wei
Keyword(s):  
Numerical Model ◽  
Hydrodynamic Pressure ◽  
Computational Domain ◽  
System Transformation ◽  
Modeling And Analysis ◽  
Gas Seals ◽  
Groove Seal ◽  
Shallow Groove ◽  
Regular Region ◽  
Volume Method

By Changing the key points on the spiral curve, general groove geometry was determined. Considering the simplicity of modeling and analysis, cubic spline function was used to express the general groove profile. By using the boundary fitted coordinate system transformation, irregular computational domain was transferred to regular region; Based on flow conservation principle, finite volume method was applied to discrete compressible Reynolds equation; By the application of Newton-Raphson iteration method for solving algebraic equation, numerical model of general groove dry gas seals was established. When compared sample results with shallow groove theory, the capacity and stiffness of numerical results match well with theoretical ones, verifying the accuracy of novel numerical model. Through analysis of three typical groove seals, spiral groove seal has strongest carrying capacity. Pressure distribution of three groove seals subjects to the law of hydrodynamic pressure effect. And the numerical model established in this paper will offer a general calculate platform for optimization of groove geometry in the future.

Pressure Drop Characteristics of Parallel-Plate Channel Flow With Porous Obstructions at Both Walls

2003 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Luzia A. Tofaneli
Keyword(s):  
Numerical Solutions ◽  
Control Volume ◽  
Computational Domain ◽  
Algebraic Equations ◽  
Clear Fluid ◽  
Simple Method ◽  
Periodic Cell ◽  
Porosity And Permeability ◽  
Volume Method ◽  
Turbulence Transport

In this work, numerical solutions are presented for turbulent flow in a channel containing fins made with porous material. The condition of spatially periodic cell is applied longitudinally along the channel. A macroscopic tow-equation turbulence model is employed in both the porous region and the clear fluid. The equations of momentum, mass continuity and turbulence transport equations are written for an elementary representative volume yielding a set of equations valid for the entire computational domain. These equations are discretized using the control volume method and the resulting systems of algebraic equations is relaxed with the SIMPLE method. Results are presented for the velocity field as a function of Reynolds number, porosity and permeability of the fins.

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