Using the composite Riemann problem solution for capturing interfaces in compressible two-phase flows (original) (raw)
Related papers
On the dynamics of a shock-bubble interaction ABSTRACT Multi-fluid flows are found in many applications in engineering and physics. Examples of these flows from engineering are water-air flows in ship hydrodynamics, exhaust-air flows behind rockets, gas-petrolea flows in upstream pipes of oil rigs, air-fuel bubble interaction flows in scramjets and many others. To gain better insight in the behavior of multi-fluid flows, especially two-fluid flows, numerical simulations are needed. We assume that the fluids do not mix or chemically react, but remain separated by a sharp interface. With these assumptions a model is developed for unsteady, compressible two-fluid flow, with pressures and velocities that are equal on both sides of the interface. The model describes the behavior of a numerical mixture of the two fluids (not a physical mixture). This kind of interface modeling is called interface capturing. Numerically, the interface becomes a transition layer between both fluids. The model consists of five equations; mass, momentum and energy equation for the mixture (these are the standard Euler equations), mass equation for one of the two fluids and energy equation for one of the two fluids. This last equation is not conservative, but contains a source term. The source term represents the exchange of energy between the two fluids. The model is discretized by using a finite-volume approximation. The finite-volume method consists of a third-order Runge-Kutta scheme for temporal discretization and a limited second-order spatial discretization. For the flux evaluation Osher's Riemann solver is constructed, which uses a new set of Riemann invariants that was derived for the two-fluid model. The source term is evaluated using the limited state distribution and the wave pattern in the Osher solver. The two-fluid model is validated on several shock tube problems. The results show that the method is pressureoscillation-free without special precautions, which is not the case for most other two-fluid flow models. The developed method is applied to two shock-bubble interaction problems. The numerical results really show the competence of the two-fluid model.
Diffuse interfaces and capturing methods in compressible two-phase flows
2017
Simulation of compressible gas dynamics flows became routinely with the appearance of capturing methods. These methods have the capability to compute routinely all waves and in particular discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows since each phase or material is governed by its own equation of state with discontinuous thermodynamic representation at interfaces. To overcome this difficulty, augmented systems of governing equations have been developed to extend the shock-discontinuity capturing strategy. These extended systems are ‘diffuse interfaces’ models, in the sense that they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they couple correctly the dynamics of the two fluids evolving on both sides of the (diffuse) interface and tend to the proper fluid governing equations far from said interfaces. Such strategy is now efficient for contact interfaces se...
Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows
Annual Review of Fluid Mechanics, 2018
Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid–governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluid...
1986
The "Generalized Riemann Problem" (GRP) method is applied to 1-D compressible flows with material interfaces and variable cross-section. The resulting scheme is second-order and uses a "mixed-type" grid, where cell boundaries can be either Lagrangian or Eulerian. In fact, using the analytic resolution of discontinuities at cell boundaries, provided by the GRP solution, one can extend the scheme presented here to include any adaptive mesh. Two numeric.al examples are studied: a planar shock-tube and an exploding helium sphere. It is shown that discontinuities are sharply resolved while there are no oscillations in the smooth part of the flow. In particular, wave interactions, including formation of new shocks and reflection from the center of symmetry, are automatically taken care of.
On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow
Journal of Computational Physics, 2009
In this work, the HLLC Riemann solver, which is much more robust, simpler and faster than iterative Riemann solvers, is extended to obtain interface conditions in sharp-interface methods for compressible multi-fluid flows. For interactions with general equations of state and material interfaces, a new generalized Roe average is proposed. For single-phase interactions, this new Roe average does not introduce artificial states and satisfies the Uproperty exactly. For interactions at material interfaces, the U-property is satisfied by introducing ghost states for the internal energy. A number of numerical tests suggest that the proposed Riemann solver is suitable for general equations of state and has an accuracy comparable to iterative Riemann solvers, while being significantly more robust and efficient.
The Explicit Simplified Interface Method for Compressible Multicomponent Flows
SIAM Journal on Scientific Computing, 2005
This paper concerns the numerical approximation of the Euler equations for multicomponent flows. A numerical method is proposed to reduce spurious oscillations that classically occur around material interfaces. It is based on the "Explicit Simplified Interface Method" (ESIM), previously developed in the linear case of acoustics with stationary interfaces (2001, J. Comput. Phys. 168, pp. 227-248). This technique amounts to a higher order extension of the "Ghost Fluid Method" introduced in Euler multicomponent flows (1999, J. Comput. Phys. 152, pp. 457-492). The ESIM is coupled to sophisticated shock-capturing schemes for time-marching, and to level-sets for tracking material interfaces. Jump conditions satisfied by the exact solution and by its spatial derivative are incorporated in numerical schemes, ensuring a subcell resolution of material interfaces inside the meshing. Numerical experiments show the efficiency of the method for rich-structured flows.
The " Generalized Riemann Problem " (GRP) method is applied to 1-D compressible Rows with material interfaces and variable cross section. The resulting scheme is second-order and uses a " mixed-type " grid, where cell boundaries can be either Lagrangian or Eulerian. In fact, using the analytic resolution of discontinuities at cell boundaries, provided by the GRP solution, one can extend the scheme presented here to include any adaptive mesh. Two numerical examples are studied: a planar shock-tube and exploding helium sphere. It is shown that discontinuities are sharply resolved while there are no oscillations in the smooth part of the flow. In particular, wave interactions, including formation of new shocks and reflection from the center of symmetry, are automatically taken care of.
A Riemann Problem Based Method for the Resolution of Compressible Multimaterial Flows
Journal of Computational Physics, 1997
A correction for Godunov-type methods is described, yielding a perfect capture of contact discontinuities, in hydrodynamic flow regime. The correction is based upon a simple idea: starting from a nondegraded solution at a given instant, the use of an Eulerian scheme around a contact discontinuity will entail, at the next instant, the degradation of the solution at only the two adjacent nodes to the discontinuity. The exact solution of the Riemann problem yields the state variables on both sides of the discontinuity. Knowledge of these variables may be used to correct the two nodes affected by numerical diffusion. The method is applied to problems involving a gas-liquid interface. The liquid is assumed compressible, obeying the ''stiffened gas'' equation of state, for which the solution of the Riemann problem is easily obtained. The method is first tested with 1D problems which have either an exact solution or accurate numerical solutions in the literature. Then the concept is extended in two dimensions. Assuming that the 1D Riemann problem along the normal to the interface is a reasonable approximation of the 2D Riemann problem for Euler equations, we extend efficiently the algorithm for two-dimensional interface problems. Several two-dimensional test cases are presented for which the method provides accurate solutions.
On the composite Riemann problem for multi-material fluid flows
International Journal for Numerical Methods in Fluids, 2014
We develop an Eulerian fixed grid numerical method for calculating multi-material fluid flows. This approach relates to the class of interface capturing methods. The fluid is treated as a heterogeneous mixture of constituent materials, and the material interface is implicitly captured by a region of mixed cells that have arisen owing to numerical diffusion. To suppress this numerical diffusion, we propose a composite Riemann problem (CRP), which describes the decay of an initial discontinuity in the presence of a contact point between two different fluids, which is located off the initial discontinuity point. The solution to the CRP serves to calculate multi-material no mixed numerical flux without introducing any material diffusion. We discuss the CRP solution and its implementation in the multi-material fluid Godunov method. Numerical results show that a simple framework of the CRP greatly improves capturing material interfaces in the Godunov method and reproduces many of the advantages of more complicated interface tracking multi-material treatments.
Physics of Fluids, 2021
Firstly, a new reconstruction strategy is proposed to improve the accuracy of the fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme. It has been noted that conventional WENO schemes still suffer from excessive numerical dissipation near critical regions. One of the reasons is that they tend to under-use all adjacent smooth sub-stencils thus fail to realize optimal interpolation. Hence in this work, a modified WENO (MWENO) strategy is designed to restore the highest possible order interpolation when three target sub-stencils or two target adjacent sub-stencils are smooth. Since the new detector is formulated under the original smoothness indicators, no obvious complexity and cost are added to the simulation. This idea has been successfully implemented into two classical fifth-order WENO schemes, which improve the accuracy near the critical region but without destroying essentially non-oscillatory properties. Secondly, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is introduced as another reconstruction candidate to better represent the discontinuity. Finally, the MWENO and THINC schemes are implemented with the Boundary Variation Diminishing (BVD) algorithm to further minimize the numerical dissipation across discontinuities. Numerical verifications show that the proposed scheme accurately capture both smooth and discontinuous flow structures simultaneously with high-resolution quality. Meanwhile, the presented scheme effectively reduce numerical dissipation error and suppress spurious numerical oscillation in the presence of strong shock or discontinuity for compressible flows and compressible two-phase flows.