Monotone Upstream-centered Schemes For Conservation Laws Research Articles

High-order discretization–based self-adaptive turbulence eddy simulation for supersonic base flow with PHengLEI software

PurposeThe purpose of the present study is to develop a new numerical framework that can predict the supersonic base flow more accurately, including the development of axisymmetrically separated shear layer and recompression shock. To this end, two aspects are improved and combined, i.e. a newly self-adaptive turbulence eddy simulation (SATES) turbulence modeling method and a high-order discretization numerical scheme. Furthermore, the performance of the new numerical framework within a general-purpose PHengLEI software is assessed in detail.Design/methodology/approachSatisfactory prediction of the supersonic separated shear layer with unsteady wake flow is quite challenging. By using a unified turbulence model called SATES combining high-order accurate discretization numerical schemes, the present study first assesses the performance of newly developed SATES for supersonic axisymmetric separation flows. A high-order finite differencing-based compressible computational fluid dynamics (CFD) code called PHengLEI is developed and several different numerical schemes are used to investigate the effects on shock-turbulence interactions, which include the monotonic upstream-centered scheme for conservation laws (MUSCL), weighted compact nonlinear scheme (WCNS) and hybrid cell-edge and cell-node dissipative compact scheme (HDCS).FindingsCompared with the available experimental data and the numerical predictions, the results of SATES by using high-order accurate WCNS or HDCS schemes agree better with the experiments than the results by using the MUSCL scheme. The WCNS and HDCS can also significantly improve the prediction of flow physics in terms of the instability of the annular shear layer and the evolution of the turbulent wake.Research limitations/implicationsThe small deviations in the recirculation region can be found between the present numerical results and experimental data, which could be caused by the inaccurate incoming boundary layer condition and compressible effects. Therefore, a proper incoming boundary layer condition with turbulent fluctuations and compressibility effects need to be considered to further improve the accuracy of simulations.Practical implicationsThe present study evaluates a high-order discretization-based SATES turbulence model for supersonic separation flows, which is quite valuable for improving the calculation accuracy of aeronautics applications, especially in supersonic conditions.Originality/valueFor the first time, the newly developed SATES turbulence modeling method combining the high-order accurate WCNS or HDCS numerical schemes is implemented on the PHengLEI software and successfully applied for the simulations of supersonic separation flows, and satisfactory results are obtained. The unsteady evolutions of the supersonic annular shear layer are analyzed, and the hairpin vortex structures are found in the simulation.

A very high order Flux Reconstruction (FR) method for the numerical simulation of 1-D compositional fluid flow model in petroleum reservoirs

Compositional reservoir simulation is an extremely important tool for modeling the fluid flow in complex petroleum reservoirs, as in cases where the reservoir fluid is volatile and composed of several pseudo-components with distinct characteristics, or reservoirs that require the use of enhanced oil recovery process. For these cases, simpler black-oil models are not suitable. The compositional model involves the solution of a large system of partial differential equations, that comprises the mass conservation, the Darcy’s law and the fugacity constraints. However, the high number of equations and constraints render the compositional problems extremely complex and computationally demanding solutions. To improve accuracy and reduce the high computational costs, one can use higher than first or even second-order methods to approximate the advective flux terms in the hyperbolic conservation laws that describe the multicomponent transport in the reservoir. Those very high-order schemes can replace low-order approaches, such as the First Order Upwind (FOU) method, which is traditionally used in commercial petroleum reservoir simulators (CMG, 2019; ECLIPSE, 2022), obtaining more accurate solutions with reduced computational cost. In this work, we consider a three-phase and isothermal fluid flow of water, oil and gas and assume that there is no mass transfer between the water and the hydrocarbon phases. Physical dispersion and capillary effects are neglected. To solve the system of Partial Differential Equations (PDEs), we used the classical IMPEC (Implicit Pressure Explicit Composition) approach and, to model the complex phase behavior, we used the Peng–Robinson equation of state (PR-EOS). The classical Two Point Flux Approximation (TPFA) method is used to spatially discretize the diffusion terms in the pressure equation. For the first time in literature the very high order Flux Reconstruction (FR) method is adapted for the numerical simulation of the compositional model in petroleum reservoirs. The FR method is a numerical scheme employed to discretize the hyperbolic conservation laws using general grids. To avoid spurious oscillations in the vicinity of solution discontinuities, the h-MLP (hierarchical Multi-dimensional Limiting Process) is applied in the reconstruction stage. For the time integration, we have used the third-order Runge–Kutta approach. To appraise the robustness of our formulation, we have solved some one-dimensional benchmark problems found in literature and compared the FR solution with the FOU method and with the second-order Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) method. From our results, the FR method has shown improved accuracy, efficiency and capability of detecting sharper shocks when compared to the other methods that we have considered for the numerical modeling of the compositional flow in the present paper.

Spectral difference method with a posteriori limiting: application to the Euler equations in one and two space dimensions

ABSTRACTWe present a new numerical scheme which combines the spectral difference (SD) method up to arbitrary high order with a-posteriori limiting using the classical MUSCL-Hancock scheme as fallback scheme. It delivers very accurate solutions in smooth regions of the flow while capturing sharp discontinuities without spurious oscillations. We exploit the strict equivalence between the SD scheme and a finite-volume scheme based on the SD control volumes to enable a straightforward limiting strategy. At the end of each stage of our high-order time-integration ADER (Arbitrary high order using Derivatives) scheme, we check if the high-order solution is admissible under a number of numerical and physical criteria. If not, we replace the high-order fluxes of the troubled cells by fluxes from our robust second-order MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) fallback scheme. We apply our method to a suite of test problems for the one-dimensional and two-dimensional Euler equations. We demonstrate that this combination of SD and ADER provides a virtually arbitrary high order of accuracy while at the same time preserving good sub-element shock capturing capabilities.

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Two-phase flow in porous media is a very active field of research, due to its important applications in groundwater pollution, {text {CO}}_2 sequestration, or oil and gas production from petroleum reservoirs, just to name a few of them. Fractional flow equations, which make use of Darcy’s law, for describing the movement of two immiscible fluids in a porous medium, are among the most relevant mathematical models in reservoir simulation. This work aims to solve a fractional flow model formed by an elliptic equation, representing the spatial distribution of the pressure, and a hyperbolic equation describing the space-time evolution of water saturation. The numerical solution of the elliptic part is obtained using a finite-element (FE) scheme, while the hyperbolic equation is solved by means of two different numerical approaches, both in the finite-volume (FV) framework. One is based on a monotonic upstream-centered scheme for conservation laws (MUSCL)-Hancock scheme, whereas the other makes use of a weighted essentially non-oscillatory (ENO) reconstruction. In both cases, a first-order centered (FORCE)-alpha numerical scheme is applied for intercell flux reconstruction, which constitutes a new contribution in the field of fractional flow models describing oil-water movement. A relevant feature of this work is the study of the effect of the parameter alpha on the numerical solution of the models considered. We also show that, in the FORCE-alpha method, when the parameter alpha increases, the errors diminish and the order of accuracy is more properly attained, as verified using a manufactured solution technique.

Lax-Wendroff method for incompressible flow

The Lax-Wendroff scheme is extended to incompressible fluid flow problems within the framework of artificial compressibility method (ACM) utilizing a “cell-centered finite-volume” Δ-approximation on a non-orthogonal non-staggered grid. An ACM induces a transformation between conservative and primitive variables; the physical relevance of ACM is to bring about “matrix preconditionings”, provoking density perturbations. The coupled algorithm is pressure-based; it benefits from enhanced accuracy and greater flexibility using the “monotone upstream-centered schemes for conservation laws (MUSCL)” approach. Numerical experiments in reference to “buoyancy-driven” flows with strong sources illustrate that the entire strategy augments overall damping capability and robustness adhering to the factored pseudo-time integration method. Conclusively, the associated limiter function has little influence on the high resolution for selected test cases.

Application of High-Order WENO Scheme in the CFD/FW–H Method to Predict Helicopter Rotor Blade–Vortex Interaction Tonal Noise

The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation of the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting rotor BVI noise using a high-resolution numerical method based on the Reynolds-averaged Navier–Stokes and the Ffowcs Williams–Hawkings equations. The seventh-order improved WENO-Z scheme is utilized to minimize the inherent numerical dissipation of the reconstruction method in the monotone upstream-centered scheme for conservation laws (MUSCL), thereby improving the rotor wake resolution and the BVI noise-prediction accuracy. The three-layer dummy cell method is used to ensure that the flux at the boundary maintains seventh-order accuracy. The effectiveness of the flow solver and the acoustic solver is validated using the Helishape-7A rotor and the UH-1H rotor, respectively. The flow field and BVI noise characteristics of the OLS rotor obtained from the fifth- and seventh-order WENO-Z schemes are compared with that of the third-order MUSCL for coarse and fine background grids. The wake resolution, noise-prediction accuracy, and computational cost of the three schemes are compared. The results show that the high-order WENO scheme provides higher accuracy for flow field simulation and BVI noise prediction than the MUSCL, but the computational cost of the WENO scheme increases substantially as the grid resolution increases. However, the WENO scheme can predict BVI using a coarser grid than the MUSCL. The computational cost of the WENO scheme is relatively low under the same flow field simulation resolution.

Fully compressible multiphase model for computation of compressible fluid flows with large density ratio and the presence of shock waves

We propose a fully compressible multiphase model for simulating compressible interfacial flows. The mathematical model is formulated on the basis of the typical conservation laws for mixtures, including mass, momentum, and energy balance. The mass balance equation in each phase is considered to discretely conserve the mass of each phase; therefore, it is always mass conservative for each phase. The numerical solution procedure for this model is developed using a high-resolution shock-capturing finite-volume method based on the Harten–Lax–van Leer-contact (HLLC) Riemann solver and total variation diminishing (TVD) time-integration schemes for simulating unsteady multiphase flows and capturing strong shocks. The finite-volume Riemann solver is combined with a monotonic upstream-centered scheme for conservation laws (MUSCL) and compressive limiters to maintain a sharp interface. The numerical framework yields a conceptually simple but robust and versatile numerical procedure. Numerical results of benchmark Riemann problems demonstrate the ability of the proposed method to obtain sharp interfaces, free of spurious oscillations, high accuracy, conservation properties, and thermodynamic consistency over various Mach numbers.

Numerical simulation of compressible multiphase hydrodynamic problems using reduced five-equation model on body-fitted grids

This paper focuses on the numerical simulation of compressible multiphase hydrodynamic problems on body-fitted mapped grids. Assuming the mixture of water and gas with homogeneous mixture properties, the reduced five-equation model (Kapila et al., 2001) is utilized to simulate the flow. Meanwhile, to circumvent the difficulties during computation such as preserving the volume fraction positivity, the pressure relaxation method (Saurel et al., 2009) is adopted to improve the robustness. The method is extended by considering the gravity effect and axisymmetric flows which are absent in the original model. A Godunov method based on the monotone upstream-centered scheme for conservation laws (MUSCL) is utilized to discretize the governing equations and the HLLC approximate Riemann solver is used to compute the numerical flux across a mesh cell face. Source terms representing the effect of gravitational and axisymmetric flow are calculated by the Runge–Kutta method. Several test cases including water–air shock tubes, dam break, underwater explosion, water entry of a hemisphere and an oblique cylinder are presented in the paper. The results obtained agree well with the exact solutions, experimental results, and other numerical computations, demonstrating the capability of the current method to deal with multiphase hydrodynamic problems involving complex geometries.

Research on Computational Method of Supersonic Inlet/Isolator Internal Flow

In this research, a CFD solver is developed for solving the 2D/3D compressible flow problem: the finite volume method based on multi-block structural grids is used to solve the compressible Reynolds averaged Navier–Stokes equations (RANS). Included in the methodology are multiple high-order reconstruction schemes, such as the 3rd-order MUSCL (Monotone Upstreamcentered Schemes for Conservation Laws), 5th-order WENO (Weight Essentially Non-Oscillatory), and 5th-order MP (Monotonicity-Preserving) schemes. Of the variety of turbulence models that are embedded, this solver is mainly based on the shear stress transport model (SST), which is compatible with OpenMP/MPI parallel algorithms. This research uses the CFD solver to conduct steady-state flow simulation for a two-dimensional supersonic inlet/isolator, incorporating these high-precision reconstruction schemes to accurately capture the shock wave/expansion wave interaction and shock wave/turbulent boundary layer interaction (SWTBLI), among other effects. By comparing the 2D/3D computation results of the same inlet configuration, it is found that the 3D effects of the side wall cannot be ignored due to the existing strong lateral flow near the corner. To obtain a more refined turbulence simulation, the commercial software ANSYS Fluent 18.0 is used to carry out the detached eddy simulation (DES) and the large eddy simulation (LES) of the same supersonic inlet, so as to reveal the flow details near the separation area and boundary layers.

Development of artificial compressibility method with elliptic relaxation approach

An artificial compressibility (AC) method resorting to the pressure-based algorithm is developed on a non-orthogonal non-staggered grid using a cell-centered finite-volume Δ-approximation for incompressible fluid flow problems. A pressure time-derivative is used to perturb the equation of continuity. This artifact provokes a density preconditioning which transforms conservative variables to primitive ones; the physical relevance of density preconditioning signifies to convoke compatible linearizations of residuals in collaboration with an AC parameter. The avoidance of pressure-velocity decoupling is enhanced by a consistently formulated cell-face dissipation approach, preserving an increased accuracy with a greater flexibility analogous to the MUSCL (monotone upstream-centered schemes for conservation laws) approach. An elliptic-relaxation scheme having accountability to promoting anisotropic diffusion coefficients is applied to smooth out the pressure residual. Numerical experiments dictate that pertaining to the pseudo-time integration method, the overall contrivance is benefited with an enhanced robustness having sensible oscillation damping characteristics.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Numerical simulations on propane/oxygen detonation in a narrow channel using a detailed chemical mechanism: formation and detailed structure of irregular cells

Numerical simulations of two-dimensional inviscid detonations for a stoichiometric propane/oxygen gas mixture are performed using a detailed chemical reaction model. The UC San Diego model which includes 57 chemical species and 268 elementary reactions is mainly used in the present study. It is shown that a grid size of 3 µm can capture important features such as the unburned gas pocket behind the detonation when compared to larger grid sizes. The effects of channel width show that the detonation propagates with the CJ (Chapman–Jouguet) velocity for all cases and for more than 100 times the channel width of 4.5 mm. Increasing the channel width results in an irregular detonation cell structure. A transverse detonation forms with cross-hatching marks on the maximum pressure history. The irregular detonation cell structure forms because both the reduced activation energy and the stability parameter have a value of approximately 10; however, the maximum thermicity in the detonation is one. The free radicals C3H7 and H2O2 play an important role in the propane oxidation under the high temperature in the detonation. The maximum concentration exists at a temperature of 2000–3000 K. The fifth-order WCNS (weighted compact nonlinear scheme) scheme can resolve the contact surface and complicated flow structure behind the detonation front compared to the second-order MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws).

A 3-D pseudo-arc-length moving-mesh method for numerical simulation of detonation wave propagation

In this paper, we propose a robust pseudo-arc-length moving-mesh method (PALM) which adopts the strategy of overall movement and block calculation for numerical simulation of detonation wave propagation in three dimensions. The pseudo-arc-length moving-mesh method involves governing equations’ evolution, mesh redistribution, and positivity-preserving analysis. Second-order finite-volume schemes and multistage total-variation-diminishing Runge–Kutta methods are used for governing equations’ evolution, while mesh redistribution is an iterative procedure that includes mesh point redistribution and cell average conservative interpolation. In addition, positivity-preserving analysis is discussed to avoid the density or pressure becoming negative in the process of numerical calculation. Finally, several numerical examples show that our method is feasible and effective. The advantage of the PALM scheme is that we can get similar results as the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) which requires more cells and computational run time. It is demonstrated that the computational grids using the PALM scheme can capture the detonation front.

A truncation error analysis of third‐order MUSCL scheme for nonlinear conservation laws

AbstractThis article is a rebuttal to the claim found in the literature that the monotonic upstream‐centered scheme for conservation laws (MUSCL) cannot be third‐order accurate for nonlinear conservation laws. We provide a rigorous proof for third‐order accuracy of the MUSCL scheme based on a careful and detailed truncation error analysis. Throughout the analysis, the distinction between the cell average and the point value will be strictly made for the numerical solution as well as for the target operator. It is shown that the average of the solutions reconstructed at a face by Van Leer's ‐scheme recovers a cubic solution exactly with , the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term is already sufficiently small with a third‐order truncation error. Finally, noting that the target spatial operator is a cell‐averaged flux derivative, we prove that the leading truncation error of the MUSCL finite‐volume scheme is third‐order with . The importance of the diffusion scheme is also discussed: third‐order accuracy will be lost when the third‐order MUSLC scheme is used with an incompatible fourth‐order diffusion scheme for convection‐diffusion problems. Third‐order accuracy is verified by thorough numerical experiments for both steady and unsteady problems. This article is intended to serve as a reference to clarify confusions about third‐order accuracy of the MUSCL scheme, as a guide to correctly analyze and verify the MUSCL scheme for nonlinear equations, and eventually as the basis for clarifying high‐order unstructured‐grid schemes in a subsequent article.

An interface-sharpening method with adaptive mesh refinement for volume-of-fluid simulations of two-phase compressible flows

We propose an interface-sharpening method for volume-of-fluid simulations of two-phase compressible flows. In the proposed method, sharpening of the interface between two phases is achieved by introducing a source term to the advection-reaction equation for the phase volume fraction. The inherent numerical diffusivity arising from the discretization of this equation is used to construct the source term. The resulting governing equations of the two-phase compressible flow are quasi-conservative and hyperbolic, with the phase volume fraction being bounded and free of spurious oscillations. The proposed method, called advection-reaction interface sharpening (ARIS), can be applied inline so that no post-processing of the phase volume fraction is required after each time step. The conservation equations for mass, momentum and energy are solved with a dimensional-splitting Monotone Upstream-centered Scheme for Conservation Laws (MUSCL). The interfacial resolution is improved by combining a fully-threaded-tree algorithm with adaptive mesh refinement. In validation tests performed on a variety of one- and two-dimensional benchmark flows, we find that ARIS can reduce the interface thickness to just three to four computational cells, improving the interfacial resolution without sacrificing computational efficiency. This study shows that ARIS can provide robust, quasi-conservative, oscillation-free and nearly sharp solutions of the phase volume fraction in various one- and two-dimensional interfacial flows, paving the way for extensions of this method to three-dimensional flows with more than two phases.

3D cell-centered Lagrangian second order scheme for the numerical modeling of hyperelasticity system

The extension of the 3D cell-centered Finite Volume EUCCLHYD scheme to the hyperelasticity system is proposed here. This study is based on the left Cauchy-Green tensor B which enables to work in a fully updated Lagrangian formalism. The second order extension of this scheme is proposed using a MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) procedure combined with a GRP (Generalized Riemann Problem) approach. In particular, the limitation of the tensor fields is done in a component-wise manner. Moreover, the complete GRP procedure is proposed in the case of Neo-Hookean compressible solids. The scheme is validated on several test cases introducing small as well as large deformations. In particular, good results are found on the non trivial problems of oscillating and twisting beams.

An Extended Eddy-Preserving Scheme for Strong Vortical Flows

Abstract The eddy-preserving limiter has been demonstrated to outperform the conventional van Albada limiter for monotone upstream-centered schemes for conservation laws (MUSCL) for vortical flows. It reduces the dissipation by inactivating the conventional van Albada limiter in the interpolation of velocity components on the swirl plane of the vortex. In this work, we extend the limiter for the interpolation of pressure since a minimum pressure often exists along the axis of a free vortex. Three-dimensional vortex advection cases are employed to demonstrate the effects of the novel scheme. An extended eddy-preserving limiter scheme has been demonstrated to further improve the preservation of the pressure extrema. Finally, the scheme is applied to flow through a draft tube and the numerical results are compared against experimental data.

Efficient three-equation two-phase model for free surface and water impact flows on a general curvilinear body-fitted grid

In this work, a simple and efficient three-equation two-phase model is transformed to a multi-dimensional general curvilinear coordinate system for simulation of free surface and water impact flows on curvilinear body-fitted grids. The two-phase model is a reduced version of the Baer–Nunziato model for compressible multiphase flows, in which the governing equations for only the liquid phase are active, whereas those for the air phase are neglected. The CPU cost is significantly reduced by solving the equation system only in the liquid regions, instead of solving the entire computational domain as in classical Euler approaches. The physical system is formulated in a hyperbolic vector form in a curvilinear coordinate system and solved using a monotonic upstream-centered scheme for conservation laws (MUSCL)/Godunov-type finite volume scheme. Compressive MUSCL limiters combined with the high-order finite volume approach result in a sharp interface solution. Validations with numerical grid refinement and convergence studies on dam-break and water impact problems are addressed, and the capability and robustness of the present model for accurate simulation of free surface and water impact flows are demonstrated. The implementation of the present system on a curvilinear body-fitted grid and the use of the Tait equation of state for water for the closure of the compressible system allow the method to solve water impact flow problems with both low-speed and high-speed complex geometries in industry and engineering.

Numerical simulation of a bulb turbine with an eddy-preserving limiter scheme

The eddy-preserving limiter scheme has been demonstrated to outperform the conventional van Albada limiter for Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) for vortical flows. It reduces the dissipation by inactivating the conventional van Albada limiter in the interpolations of the velocity components on the swirl plane of the vortex. In this work, we extend the limiter for the interpolation of pressure, since a minimum pressure often exists along the axis of a free vortex. The conventional van Albada limiter is inactivated in the interpolation of pressure at smooth extrema. A 3D inviscid vortex advection case is employed to demonstrate the effects of the novel scheme. The extended eddy-preserving limiter scheme has been demonstrated to be able to further minimize the dissipation of the vortex than the original eddy-preserving limiter scheme. Finally, the scheme is applied to the BulbT test case and the numerical results are compared against experimental data.

A comparative study of explicit high-resolution schemes for compositional simulations

PurposeThis paper aims to numerically study the compositional flow of two- and three-phase fluids in one-dimensional porous media and to make a comparison between several upwind and central numerical schemes.Design/methodology/approachImplicit pressure explicit composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly, whereas the mass conservation equations are solved explicitly using different upwind (UPW) and central (CEN) numerical schemes. These include classical upwind (UPW-CLS), flux-based decomposition upwind (UPW-FLX), variable-based decomposition upwind (UPW-VAR), Roe’s upwind (UPW-ROE), local Lax–Friedrichs (CEN-LLF), dominant wave (CEN-DW), Harten–Lax–van Leer (HLL) and newly proposed modified dominant wave (CEN-MDW) schemes. To achieve higher resolution, high-order data generated by either monotone upstream-centered schemes for conservation laws (MUSCL) or weighted essentially non-oscillatory (WENO) reconstructions are used.FindingsIt was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme uses most of the information in flux function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e. degenerate, umbilic and elliptic points, which require applying correction procedures to produce physically acceptable (entropy) solutions.Research limitations/implicationsThis paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids, whereas gravity and capillary effects are neglected.Practical implicationsThe proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.Originality/valueA new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.