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Application of computational fluid dynamics softwares for 2d acoustical wave
propagation
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APPLICATION OF COMPUTATIONAL FLUID DYNAMICS SOFTWARES FOR 2D ACOUSTICAL WAVE PROPAGATION
P. Tóth Ph.D. student, Department of Fluid Dynamics, Budapest University of Technology and Economics,
H-1111 Budapest, Bertalan L. u. 4-6. Tel: (+36-1) 463-2546, e-mail: [email protected]
A. Fritzsch Student in Engineering Science, Berlin Institute of Technology (TU Berlin)
D-10623 Berlin, Strasse des 17. Juni 135, e-mail: [email protected]
M. M. Lohász Assistant professor, Department of Fluid Dynamics, Budapest University of Technology and Economics, H-
1111 Budapest, Bertalan L. u. 4-6. 5. Tel: (+36-1) 463-1560, e-mail: [email protected]
Abstract: The direct noise computation approach in aeroacoustics is an important tool to
predict the noise emitted by turbulent flows. A special treatment of the solution algorithms is
needed in this case. This paper attempts to show the capabilities of two general purpose
Computational Fluid Dynamics codes in a 2D acoustical simulation of the propagation of a
pressure pulse. The effect of the time step size, grid resolution, numerical schemes, and
solution algorithms were investigated for this purpose. The test showed that the so called
density-based formulation gives the most reliable results.
Keywords: CFD, CAA, acoustic pulse
1. INTRODUCTION The recent progress in the unsteady flow simulation techniques, namely the direct
numerical and the large-eddy simulations (DNS/LES) allow the direct computation of the
sound generated by turbulent flows. However the orders of magnitudes discrepancy between
the flow and acoustic scales require special treatment in terms of numerical solution methods.
The solution method requires high accuracy spatial and temporal discretisation in order not to
wash out the small acoustical scales from the simulation. In aeroacoustics often special in-
house codes are used to overcome these problems. Therefore the applicability of general
purpose computational fluid dynamics (CFD) software for direct aeroacoustics computations
is not evident. Such codes are mainly designed to solve complex flow physics with difficult
geometry and use robust solution algorithms for arbitrary mesh topology and usually this
comes with the use of smaller accuracy numerical methods. These codes are fitted to solve
industrial fluid dynamics applications. Moreover there is an increasing demand on the noise
emission by industrially relevant flows.
With the computational resources available today only the noise generated by the
simplest flows can be calculated in the acoustical far field by the means of direct noise
computation (DNC). The computational cost of this solution method in an industrially
relevant problem is prohibitively large. Although in some cases (e.g. free shear layer flows),
where the volumetric acoustic source terms need to be taken into account, the combination of
the DNC simulation with other aeroacoustics methods (i.e integral methods) is beneficial. In
those cases the volumetric source data is computed by a DNC simulation in a relatively small
region, where the sound is produced and from the boundary of that source region another,
simpler method is used to obtain the far field acoustic signal [9]. The advantage of this
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procedure is the smaller amount of computer memory and storage capacity requirement,
because in such cases for acoustical post processing it is enough to store the source
information on the boundary of the source region instead of storing the entire volumetric
source region information. This greatly enhances the post processing of the acoustic far field
region.
In the light of the previously mentioned issues the applicability of general purpose
CFD applications in the field of direct sound computations can be an important question. If
these industrially relevant applications enable DNC in the near-field of the acoustic sources,
(with acceptable accuracy) then noise computation of complex turbulent flows (e.g.
aeroacoustics of free jet flow) could be obtained. However there are only a few guidelines (as
far as the authors know) concerning the applicable numerical methods, which can be used in a
general purpose CFD application to compute the aerodynamically generated noise by means
of DNC.
This paper attempts to show the capabilities of two general purpose CFD codes in a
2D acoustical simulation of the propagation of a pressure pulse. This is a basic aeroacoustic
test case used to validate and tune aeroacoustical solvers and boundary conditions [1,8]. The
tested two CFD codes are Fluent6.3.26 and OpenFOAM1.4.1. Below the test case is
introduced, and the two CFD applications and numerical parameters are discussed briefly.
Results obtained by different numerical methods are shown and compared to the analytical
solution of the problem. The conclusions are given at the end.
2. THE ACOUSTIC TEST CASE The quality of a numerical solution can be verified by the comparison of the results to
the analytical solution of that problem. However this analytical solution exists only for some
particular cases. In this study a 2D acoustic pulse propagation case in a uniform flow was
chosen as the test simulation. The analytical solution of this case is obtained from the
linearized Euler equations presented in [8]. The two dimensional domain is a square. A
uniform flow with Mach number M=0.5 is prescribed in one direction of the domain. The
boundary conditions are defined in order to maintain this uniform flow in the domain. An
initial perturbation, which is a Gaussian pressure distribution, is imposed at the centre of the
domain at t=0.
2
( , ,0)
( , ,0)
( , ,0) 0
p x y e
u x y M
v x y
αηρ ε −= =
=
=
(1)
, where α is related to the half width of the Gaussian profile b, by 2ln 2 / bα = , furthermore
( )1/ 2
2 2x Mt yη = − +
, which is equal to the radial coordinate in the case of t=0. (p and ρ
denotes perturbation values around the average) The Gaussian half width was b=3, and the
amplitude was ε=0.01 in this study (this small ε is needed for the lineralized equations to be a
good approximation of the nonlinear ones). The simulation domain with the initial pressure
pulse can be seen in Fig. 1 left. This kind of initial condition induces the acoustic wave mode
[2] of the underlying equations. The analytical solution of the problem for the pressure and
density can be given with a Bessel function J0 order of zero:
2 / 4
0
0
( , , ) ( , , ) cos( ) ( )2
p x y t x y t e t J dξ αε
ρ ξ ξη ξ ξα
∞−= = ∫ (2)
This solution can be seen in Fig. 1 right at t=20. The accuracy of the numerical solution was
evaluated by comparing it to this particular solution of the lineralized equations. The
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simulation variables are nondimensionalized for the post processing. For this purpose the
ambient sound velocity c0, the ambient density ρ0 and the grid spacing ∆x=∆y are used for the
velocity, density and length scale respectively. Therefore the time scale is ∆x/a0 and the
pressure scale is ρ0 c02.
Fig.1. Left: Initial pressure pulse imposed in the domain with uniform mean flow. Right:
Pressure disturbance at t=20 from the analytical solution.
3. THE SOLVERS As it was previously mentioned in this study two general purpose CFD codes are
examined for acoustic wave propagation. One of them is the commercial code Fluent 6.3.26.
The other one is an open source CFD application called OpenFOAM 1.4.1. Both codes use
collocated variable arrangement and unstructured mesh handling. However the former
contains two different solution methods: the so called “pressure-based” and the “density-
based” algorithms for the solution of the compressible Navier-Stokes (N-S) system of
equations. The OpenFOAM environment provides only “pressure-based” algorithm with the
PISO pressure velocity coupling method. The available discretisation schemes are different
except some basic methods. In both codes implicit and explicit spatial and temporal schemes
are available. An important difference between the codes is that the open source code
provides only a sequential solution method for the governing equations meaning that the
coupling between the momentum, pressure correction and energy equation is not satisfied
accurately. This introduces a so called splitting error in the solution procedure [3]. However
the open source type of the code gives the opportunity to modify the existing solver
algorithms, therefore this type of error can be reduced with the expense of higher
computational cost. The boundary conditions are different on the applied solvers. In the
present investigation attention is devoted to simulate the wave propagation accurately.
Therefore the boundary conditions are handled in the simplest way. In all simulation cases
presented here reflective boundary conditions were applied and placed at a distance where
they cannot influence the results obtained at t=20.
4. NUMERICAL SETUP The computational domain can be seen in Fig.2 left. This is a square region meshed
with uniformly distributed quadrilateral cells. The grid spacing is ∆x=∆y. The domain extends
in the 55 55x− ≤ ≤ , 55 55y− ≤ ≤ region. Mass flow inlet and velocity inlet boundary
conditions are imposed at x=-55 for the Fluent and OpenFOAM solvers, respectively. The
inlet is a uniform flow with prescribing the value of M=0.5 for the velocity and the related
total temperature. On the outflow boundary a constant pressure condition is applied which
defines the static temperature as well. The other boundaries are treated with symmetry
condition. For the time period examined it can be assumed that this does not influence the
solution, since no wave reaches this boundary. The initial conditions for the flow variables
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were prescribed by expression (1). In the underlying solvers the density distribution cannot be
directly imposed as an initial condition. The density field can be prescribed through the
constitutive equation by setting the temperature field properly. The ideal gas law is applied as
a constitutive equation. The uniform flow (u=M) was imposed towards the x direction. In all
simulations of N-S a fluid with dynamic viscosity ]ms/kg[107894.1 5−⋅=µ , specific heat
constant cp=1006.43[J/kgK], specific gas constant R=287.038[J/kgK] and thermal
conductivity λ=0.0242[W/mK] was used. The gradient formulation in the solvers was similar
based on the Gauss theorem. In the following section the results obtained by the two different
solvers and by the different numerical parameters are presented.
Fig.2. Left: Simulation mesh with the boundary conditions. Right: CFL number effect on the
results with Fluent pressure-based solver (Pressure profiles extracted at the line y/∆y=0.)
5. RESULTS The simulation parameters and computed errors are summarized in Table1-3. The
simulations evaluated by the Fluent’s pressure-based solver can be seen in Table1, the
density-based solver parameters in Table 2 and the details of the OpenFOAM simulations
with coodles solver in Table 3. A unique identifier is assigned to every simulation which is
depicted in the first column of the tables. The discretisation issues are divided into two parts
the spatial discretisation and the temporal one. Below the spatial discretisation tag the grid
size parameter ( / 6bδ ≅ ) and the name of the discretisation schemes used for the convective
and pressure terms of the equations can be found. In Table 2 only one scheme is depicted for
spatial discretisation because of the density-based approach. Under the temporal discretisation
tag the flow CFL number (see Eqn. 4) and the name of the scheme are indicated. In the next
column the pressure velocity coupling for the pressure-based solver and the flux formulation
method for the density-based solver are presented. The solution algorithm column refers to
the previously mentioned iterative (ITA) or non-iterative (NITA) method. For the density-
based explicit formulation nothing is presented in Table 2 indicating the explicit treatment. In
the last columns of the tables the simulation error computed as a comparison to the analytical
solution is depicted.
( )
2
2
ana
ana
p p dAErr
p dA
−=∫∫∫∫
(3)
Here pana is the analytical solution on the domain, and p is the numerically computed value.
The integration is taken on the whole 2D computational domain.
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Spatial discretisation Temporal discretisation
Case
Grid
∆x,∆y
Convective
term
Pressure CFL
Scheme
Pressure velocity coupling
Solution algorithm
Err
Fp1 δ BCD PRESTO 0.075 imp.
Gear
FSM NITA 1.10844
Fp2 δ BCD PRESTO 0.15 imp.
Gear
FSM NITA 0.32915
Fp3 δ BCD PRESTO 0.24 imp.
Gear
FSM NITA 0.33541
Fp4 δ BCD PRESTO 0.3 imp.
Gear
FSM NITA 0.34655
Fp5 δ BCD PRESTO 0.6 imp.
Gear
FSM NITA 0.80521
Fp6 δ BCD Linear 0.24 imp.
Gear
FSM NITA 0.28625
Fp7 δ BCD second
ord.
0.24 imp.
Gear
FSM NITA 0.24071
Fp8 δ BCD standard 0.24 imp.
Gear
FSM NITA 0.90848
Fp9 δ Den., En.:
SOU
Mom.: BCD
PRESTO 0.24 imp.
Gear
FSM NITA 0.37289
Fp10 δ Den., En.:
QUICK
Mom.: BCD
PRESTO 0.24 imp.
Gear
FSM NITA 0.37051
Fp11 δ Den., En.:
MUSCL
Mom.: BCD
PRESTO 0.24 imp.
Gear
FSM NITA 0.37025
Fp12 δ BCD PRESTO 0.24 imp.
Gear
coup. ITA 0.21625
Fp13 δ BCD PRESTO 0.24 imp.
Gear
PISO ITA 0.21625
Fp14 δ BCD PRESTO 0.24 imp.
Gear
Simple ITA 0.21625
Fp15 δ/2 BCD PRESTO 0.24 imp
Gear
FSM NITA 0.16657
Fp16 δ/2 BCD second
order
0.24 imp
Gear
FSM NITA 0.11680
Fp17 δ/4 BCD PRESTO 0.24 imp.
Gear
FSM NITA 0.13031
Tab.1. Comparison table for the simulations with Fluent’s pressure-based solver.
Fluent pressure-based solver The first test is devoted to clarify the effect of the CFL number. The CFL number
takes the local convection speed of a disturbance in the flow, the grid spacing, and the time
step into account. It determines conditions for the maximum time step value in order to reach
reasonable temporal accuracy:
( )u c t
CFLx
+ ∆=
∆ (4)
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Five simulations with the same numerical parameters except the time step were accomplished
on the test case. The result is presented in Table 1. Fp1-Fp5. The Bounded Central
Differencing scheme (BCD) is used for the convective terms [5]. For the pressure term the
Pressure Staggering Option (PRESTO) is applied [4]. The pressure velocity coupling is based
on the Fractional Step method (FSM) [3] with the non-iterative time advancement solution
method (NITA) [4]. It can be seen in the table that the simulation error has minimum value at
CFL=0.15. Decreasing the time step further resulted in higher error and spurious oscillations
in the resulting flow field Fig 2 right. It will be matter of further investigation if this error is
due to the increased impact of the rounding errors on the simulation (i.e more time-steps are
needed to reach the end of the simulation which can be result in the accumulation of the
rounding errors [7]). The dispersion and dissipation error [3] of the pressure wave is higher at
the downstream positions. This can be seen in Fig.2 right, where the impulse at the
downstream location has smaller amplitude and it is wider than the one located upstream.
The CFL=0.24 value seemed to be an optimum in the sense of computational resource and
accuracy considerations. This value was chosen for the further investigations.
With the pressure-based solver the effect of the interpolation schemes were also investigated.
For the momentum equations the BCD scheme [5] was used in every test case due to its low
diffusion property required for the accurate simulation of the N-S equation. In terms of the
pressure interpolation schemes (Fp6-Fp8) the second order scheme [4] performed the best
(Table 1 Fp7). The standard scheme [4] is significantly worse than the others (Table 1. Fp8).
The linear scheme for the pressure is slightly better than the PRESTO scheme (Table 1. Fp6).
Changing the interpolation scheme for the convective terms in the energy and density
equations from BCD to MUSCL, Second order upwind (SOU) or QUICK [4] is resulting in
the increase of the simulation error. This can be seen on simulations Fp9-Fp11.
Results obtained by the iterative time advancement method using the coupled, PISO and
SIMPLE [4], pressure velocity coupling methods can be seen in Table 1. Fp12 Fp13, Fp14
respectively. The iterative solution procedure reduced the solution error with the same value
independently from the coupling used between the pressure and velocity comparing to the
reference case (Fp3). This result shows the importance of the coupling between the flow
equations. The iterative solver can provide the variables are satisfying all of the equations
with good accuracy. The difference between the NITA and ITA time advancement procedures
is demonstrated on Fig 3, where the pressure and density profiles are plotted together for the
Fp3 simulation with NITA and Fp13 simulation with ITA procedure. As previously
mentioned in this test case the pressure and density have analytically the same value in each
point. It can be seen on the chart that the NITA solution procedure does not exactly satisfy
this criteria in the whole domain. The pressure and density profiles do not coincide in the
region 0<x/∆x<15 (see Fig.3 left). With the ITA method the profiles have a better overlap.
However some spurious oscillations can be found (see Fig.3 right).
The application of a twice better grid resolution (Fp15, Fp16) can help to
approximately halve the solution error. Using a four times finer grid ( Fp17) in every direction
does not reduce the error significantly indicating that mainly the splitting error in the solution
procedure influences the results, and not the spatial resolution of the underlying numerical
scheme. According to the previous tests the accuracy reached by the pressure-based solver
with the non-iterative time advancement is not satisfactory. However the computational cost
of this procedure with NITA is reasonable, which is also an important parameter. The
simulation cost for the four times smaller cell size is greatly increased, and it is highly
unpractical to use. The ITA procedure can reduce the simulation error with much higher
computational cost.
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Fig.3. Left: Pressure and density profiles of the simulation Fp3 extracted at the line y/∆y=0.
Right: Pressure and density profiles of the simulation Fp13 extracted at the line y/∆y=0.
Results obtained by the density-based solver The other simulation method offered by the Fluent solver is the density-based
algorithm. This method was originally designed for solving compressible flow problems [4].
It solves the equations in a fully coupled manner, which requires significantly greater
computer memory and usually more computation (CPU) time if implicit discretisation is used.
Whereas the explicit spatial and temporal discretisation method provides comparable
computational time requirement as the pressure-based NITA solver. The simulation results
with the density-based solver are summarized in Table 2. The results obtained by the “low
diffusion Roe” type [4] flux calculation (Fd2, Fd3) provided the lowest simulation errors. The
other methods (Roe, AUSM [4]) (Fd1, Fd4 respectively) performed worse. Considering the
simulations with the low diffusion Roe scheme the third order MUSCL (Fd3) discretisation
for the flow variables provides smaller simulation error comparing to the simulation using
first order upwind (FOU) scheme (Fd2). This is in agreement with the expectations.
Spatial discretisation Temporal
discretisation
Case
Grid
∆x,∆y
Scheme CFL Scheme
Flux type Solution
algorithm
Err
Fd1 δ SOU 0.24 Gear roe ITA 0.18759
Fd2 δ FOU 0.24 Gear low diff
roe
ITA 0.12756
Fd3 δ MUSCL 0.24 Gear low diff
roe
ITA 0.10094
Fd4 δ SOU 0.24 Gear AUSM ITA 0.16655
Fd5 δ/2 MUSCL 0.24 Gear low diff
roe
ITA 0.01762
Fd6 δ/2 FOU 0.24 Gear low diff
roe
ITA 0.02705
Fd7 δ Exp SOU 1 Rk4 Roe-FDS - 0.19249
Fd8 δ Exp SOU 0.3 Rk4 Roe-FDS - 0.17526
Fd9 δ Exp
MUSCL
1 Rk4 Roe-FDS - 0.22729
Tab.2. Comparison table for the simulations with Fluent’s density-based solver.
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Using the mesh with halved grid spacing the simulation error is reduced by one order of
magnitude. This can be seen in Table 2 Fd5, Fd6. This solution error can be accepted for
simulation of acoustic wave propagation though only on a short distance.
There is a possibility to use explicit discretisation schemes for both the spatial and the
temporal terms in the density-based solver of Fluent. The explicit solution procedure is
computationally efficient but there is a stability limit for the time step size in the simulation.
This restricts the CFL number below the value of one [4]. As previously seen the CFL
number about 0.2 is required for the accurate simulation even with the implicit solver.
Therefore this criterion can be satisfied without any increase in the required computer
resource. Simulation results (Fd7, Fd8, Fd9) obtained with fully explicit density-based solver
using the four stage Runge-Kutta time discretisation scheme (Rk4) can be found in Table 2
also. It can be observed that with the SOU spatial discretisation and with CFL=0.3 the
simulation error is smaller than the simulation results obtained with the pressure-based solver
on the same mesh. The simulation setup with CFL=1 and with the SOU or MUSCL scheme
provided almost the same simulation error that was found in the best pressure-based solver
results.
Fig.4. Left: Pressure profiles of the best simulation results with the pressure-based solver
extracted at the line y/∆y=0. Right: Pressure profiles of the best simulation results with the
density-based solver extracted at the line y/∆y=0.
The profiles of the best simulation result with the density-based solver can be seen in Fig. 4
right. The reasonable good agreement of the Fd5 simulation with the analytical solution can
be observed.
This test clearly shows the superior performance of the density-based solution method
considering that better accuracy can be achieved with lower computational cost comparing to
the pressure-based solver. If the limit for the simulation error is not very high the density-
based solver with the explicit formulation is recommended due to its low computational cost.
The OpenFOAM results The results obtained by OpenFOAM solver are summarized in Table 3 In this
environment only a pressure-based solver (called coodles) with PISO corrector loop is
available for solving the N-S equations. Basically in this solver the equations are solved
sequentially, similarly to the method of NITA used in Fluent. In the present study mainly the
effect of the temporal discretisation scheme, the CFL number and the grid resolution is
considered. The Filtered linear scheme is used for the discretisation of the convective term.
This is a modified second order central differencing scheme to prevent spurious oscillations
[6]. The pressure term is discretised with the linear scheme, which is a second order central
differencing scheme [6].
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For the simulations O6, O10 the solution algorithm is modified in order to resemble the
Fluent’s iterative algorithm.
Spatial discretisation Temporal discretisation
Case
Grid
∆x,∆y
Convective
term
Pressure CFL scheme
Pressure velocity coupling
Solution algorithm
Err
O1 δ filtered
linear
linear 0.075 Crank-
Nicholson
0.6
PISO NITA 0.27008
O2 δ filtered
linear
linear 0.15 Crank-
Nicholson
0.6
PISO NITA 0.2675
O3 δ filtered
linear
linear 0.24 Crank-
Nicholson
0.6
PISO NITA 0.27139
O4 δ filtered
linear
linear 0.3 Crank-
Nicholson
0.6
PISO NITA 0.28309
O5 δ filtered
linear
linear 0.75 Crank-
Nicholson
0.6
PISO NITA 0.37984
O6 δ filtered
linear
linear 0.15 Crank-
Nicholson
0.6
PISO ITA 0.25169
O7 δ filtered
linear
linear 0.15 Backward
Euler
PISO NITA 0.30534
O8 δ/2 filtered
linear
linear 0.3 Backward
Euler
PISO NITA 0.04916
O9 δ/2 filtered
linear
linear 0.12 Backward
Euler
PISO NITA 0.10753
O10 δ/2 filtered
linear
linear 0.12 Backward
Euler
PISO ITA 0.05486
O11 δ/2 filtered
linear
linear 0.12 Crank-
Nicholson
0.6
PISO NITA 0.05051
O12 δ/2 filtered
linear
linear 0.3 Crank-
Nicholson
0.6
PISO NITA 0.03568
O13 δ/2 filtered
linear
linear 0.12 Crank-
Nicholson 1
PISO NITA 0.10559
O14 δ/2 filtered
linear
linear 0.3 Crank-
Nicholson 1
PISO NITA 0.04551
Tab.1. Comparison table for the simulations with OpenFOAM solver.
The O1-O5 test cases are devoted to determine the optimal CFL number for the
simulation. The simulation error does not change significantly between CFL numbers from
0.075 to 0.3. The CFL value around 0.15 seems to be an optimal choice. The effect of the
CFL number on the pressure profile can be examined on Fig. 5. Overshoots can be observed
at the downstream pressure peaks. It has to be denoted, that this optimum is determined for
the implicit Crank Nicholson discretisation scheme with blending factor of 0.6 and with mesh
size of ∆x=∆y=δ. The blending factor blends the Crank Nicholson scheme into the Euler
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scheme. A coefficient of 1 corresponds to pure Crank Nicholson and 0 corresponds to pure
Euler scheme. The implicit backward Euler scheme has approximately the same error as the
Crank Nicholson scheme (see O7 in Table 3). Comparing the simulation results O8 and O9
obtained on the refined grid the effect of the CFL number is different as before. The result
evaluated by CFL=0.3 (O8) has smaller error than the one calculated using CFL=0.12 (O9).
However the O8 has an overshot at the downstream peaks of the pressure pulse as it can be
seen in Fig 5 right. The same CFL effect can be observed for the simulation cases with Crank
Nicholson scheme O11, O12 and O13, O14. Such behaviour can be disadvantageous on a
simulation with nonuniform mesh spacing and velocity distribution. The smallest simulation
error was achieved on the finer mesh with Crank Nicholson scheme with blending factor of
0.6 (simulation O12). Use of the pure Crank Nicholson (blending factor 1) scheme O14 is
resulted in a bit higher simulation error. The iterative (ITA) coupling between the equations
does not come with significant accuracy increase using the Crank Nicholson scheme (O6).
The situation is slightly better for the simulation with the Euler scheme (O10), where the ITA
procedure approximately halved the error.
Fig.5. Left: Pressure profiles showing the effect of the CFL number with OpenFOAM solver
extracted at the line y/∆y=0. Right: Pressure profiles of the best simulation results with the
OpenFOAM solver extracted at the line y/∆y=0.
6. CONCLUDING REMARKS In this paper the performance of two Computational Fluid Dynamics software packages
were investigated in an acoustic pulse propagation test case. The commercial Fluent 6.3.26
software provides a wide range of solution algorithms. From our experience the solution
results with pressure-based algorithm are showing higher dispersion and dissipation error than
the density-based solution method. For the case of the pressure-based solution these errors are
especially pronounced using the non-iterative time advancement. In the OpenFOAM1.4.1
environment only pressure-based solver is available. Comparing the Fluent pressure-based
and the OpenFOAM coodles solver the same order of error is arisen when comparing to the
analytical solution. The error reduction by grid refinement was found to be higher using
OpenFOAM than the one gain with Fluent pressure-based approach. Calculations with the
OpenFOAM solver also showed smaller dissipation and dispersion error in the test, but some
overshoot in the results can be observed. The Fluent’s density-based solver results show the
best dispersion and dissipation error properties and together with the ability for significant
error reduction when refining the grid. Further on using the explicit formulation of the
density-based algorithm the computational cost of the simulation can be acceptable as well.
As the final conclusion the use of the density-based formulation is recommended for accurate
acoustic wave propagation calculations.
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