Modification of the Riemann Problem and the Application for the Boundary Conditions in Computational Fluid Dynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00010669%3A_____%2F17%3AN0000053" target="_blank" >RIV/00010669:_____/17:N0000053 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.epj-conferences.org/articles/epjconf/abs/2017/12/epjconf_efm2017_02061/epjconf_efm2017_02061.html" target="_blank" >https://www.epj-conferences.org/articles/epjconf/abs/2017/12/epjconf_efm2017_02061/epjconf_efm2017_02061.html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/epjconf/201714302061" target="_blank" >10.1051/epjconf/201714302061</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Modification of the Riemann Problem and the Application for the Boundary Conditions in Computational Fluid Dynamics

Popis výsledku v původním jazyce

We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side). The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak) solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy), therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some cases. Moreover, using such construction, the local conservation laws are not violated. Algorithms for the solution of the modified Riemann problems were coded and used within our own developed code for the solution of the compressible gas flow (the Euler, the Navier-Stokes, and the RANS equations). Numerical examples show superior behaviour of the suggested boundary conditions. Constructed boundary conditions are robust and accelerate the convergence of the method. The original result of our work is the analysis of various modifications of the Riemann problem and its applications.

Název v anglickém jazyce

Modification of the Riemann Problem and the Application for the Boundary Conditions in Computational Fluid Dynamics

Popis výsledku anglicky

We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side). The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak) solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy), therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some cases. Moreover, using such construction, the local conservation laws are not violated. Algorithms for the solution of the modified Riemann problems were coded and used within our own developed code for the solution of the compressible gas flow (the Euler, the Navier-Stokes, and the RANS equations). Numerical examples show superior behaviour of the suggested boundary conditions. Constructed boundary conditions are robust and accelerate the convergence of the method. The original result of our work is the analysis of various modifications of the Riemann problem and its applications.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

EPJ Web of Conferences

ISBN

—

ISSN

2101-6275

e-ISSN

2100-014X

Počet stran výsledku

11

Strana od-do

nestrankovano

Název nakladatele

EDP Sciences

Místo vydání

Neuveden

Místo konání akce

Mariánské lázně

Datum konání akce

15. 11. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000407743800063