Development of a new OpenFOAM solver using regularized gas dynamic equations

Kraposhin, Matvey; Смирнова, Е. В.; Елизарова, Т. Г.; Istomina, M. A.

doi:10.1016/j.compfluid.2018.02.010

Cited by 47 publications

(24 citation statements)

References 17 publications

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“…For example, rhoCentralFoam fails to simulate low Mach number flows. Unlike other explicit OpenFOAM solvers, which uses preconditioning, eg, in the work of Heinrich and Schwarze or equations regularization, the developed one uses blending function allowing to switch to the pure PISO algorithm for zones with low Mach number. To validate our rhoPimpleCentralFoam ‐solver ability to simulate laminar subsonic flows, three cases were chosen, ie, a laminar pipe flow (also known as Poiseuille flow), a laminar flow around a cylinder, and a backward‐facing step flow in a channel.…”

Section: Resultsmentioning

confidence: 99%

A hybrid pressure‐based solver for nonideal single‐phase fluid flows at all speeds

Kraposhin

Banholzer

Pfitzner

et al. 2018

Numerical Methods in Fluids

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Summary This paper describes the implementation of a numerical solver that is capable of simulating compressible flows of nonideal single‐phase fluids. The proposed method can be applied to arbitrary equations of state and is suitable for all Mach numbers. The pressure‐based solver uses the operator‐splitting technique and is based on the PISO/SIMPLE algorithm: the density, velocity, and temperature fields are predicted by solving the linearized versions of the balance equations using the convective fluxes from the previous iteration or time step. The overall mass continuity is ensured by solving the pressure equation derived from the continuity equation, the momentum equation, and the equation of state. Nonphysical oscillations of the numerical solution near discontinuities are damped using the Kurganov‐Tadmor/Kurganov‐Noelle‐Petrova (KT/KNP) scheme for convective fluxes. The solver was validated using different test cases, where analytical and/or numerical solutions are present or can be derived: (1) A convergent‐divergent nozzle with three different operating conditions; (2) the Riemann problem for the Peng‐Robinson equation of state; (3) the Riemann problem for the covolume equation of state; (4) the development of a laminar velocity profile in a circular pipe (also known as Poiseuille flow); (5) a laminar flow over a circular cylinder; (6) a subsonic flow over a backward‐facing step at low Reynolds numbers; (7) a transonic flow over the RAE 2822 airfoil; and (8) a supersonic flow around a blunt cylinder‐flare model. The spatial approximation order of the scheme is second order. The mesh convergence of the numerical solution was achieved for all cases. The accuracy order for highly compressible flows with discontinuities is close to first order and, for incompressible viscous flows, it is close to second order. The proposed solver is named rhoPimpleCentralFoam and is implemented in the open‐source CFD library OpenFOAM®. For high speed flows, it shows a similar behavior as the KT/KNP schemes (implemented as rhoCentralFoam‐solver, Int. J. Numer. Meth. Fluids 2010), and for flows with small Mach numbers, it behaves like solvers that are based on the PISO/SIMPLE algorithm.

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Section: Resultsmentioning

confidence: 99%

A hybrid pressure‐based solver for nonideal single‐phase fluid flows at all speeds

Kraposhin

Banholzer

Pfitzner

et al. 2018

Numerical Methods in Fluids

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“…Below we consider five tests which are versions of this problem and reflect different situations in the arising flows. The tests 1-4 are well-known in the literature [4,5,9,12,16], and test 5 has recently been proposed to us by M.V. Kraposhin.…”

Section: Computations Of the Riemann Problem And Comparison Of Schemesmentioning

confidence: 99%

“…Define the mesh ω Xh = {−X/2 + kh} N k=0 with h = X/N . Below we present some brief information on solving these tests by the schemes S, A, A 1 , A 2 and B as well as also by the standard-type QGD-scheme S 0 from [4,5], which is somewhat different from the scheme S. Note that the verification of one more standard-type QGD-scheme and its comparison with the Kurganov-Tadmor scheme has recently been performed in [9]. For all schemes S, A, A 1 , A 2 and B, the results are close.…”

Section: Computations Of the Riemann Problem And Comparison Of Schemesmentioning

confidence: 99%

“…In this flow, two rarefaction waves are formed running away from the region center x = 0, where ρ and p are close to 0 (in particular, ρ(0, t f in ) ≈ 0.022 and p(0, t f in ) ≈ 0.0019) but ε does not tend to zero. Although the solution is continuous for t > 0, for a lot of schemes [12], including the scheme S 0 [4,5] and the QGD-scheme in [9], a significant unphysical local extremum of ε (an entropy wake) is observed for x = 0, which slowly decreases as N grows.…”

Section: Computations Of the Riemann Problem And Comparison Of Schemesmentioning

confidence: 99%

“…As for the schemes S, A 1 and A 2 , the solutions are destroyed in both tests even for a much smaller β = 0.001. Also, for the scheme S 0 and QGD-scheme from [9], there exist serious problems concerning the computation of solutions (M.V. Kraposhin, private communication).…”

Section: Computations Of the Riemann Problem And Comparison Of Schemesmentioning

confidence: 99%

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Verification of an Entropy Dissipative QGD-Scheme

Злотник

Ломоносов

2019

Mathematical Modelling and Analysis

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An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the previously constructed QGD-schemes and its merits are noticed. Practical convergence rates in the mesh L1-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for L2-dissipativity of the Cauchy problem for a linearized QGD-scheme.

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