Weighted Essentially Non-oscillatory Scheme Research Articles

Shock wave induced by the collapse of a bubble cluster with each bubble distributed randomly

The phenomenon of bubble collapse is ubiquitous in both natural and industrial settings, often manifesting in the form of bubble clusters. Despite its prevalence, there has been limited research on the dynamics of bubble clusters. In order to gain a better understanding of shock wave emission, liquid jet propagation, and the resulting pressure loads during bubble cluster collapse, we have developed a high-fidelity numerical approach aimed at accurately capturing shock waves and phase interfaces. The interface compression technique is introduced into the compressible two-phase model to improve the sharpness of the phase interface. We solve the physical model using the BVD (Boundary Variation Diminishing) principle. Both the 5th order WENO (Weighted Essentially Non-Oscillatory) scheme and the interface capturing function THINC (Tangent of Hyperbola for INterface Capturing) are utilized to reconstruct primary variables at cell boundaries, effectively minimizing numerical dissipation. For further resolution improvement, we implement these numerical methods on the AMR (Adaptive Mesh Refinement) mesh. Our numerical results demonstrate that the distance between the wall and the bubble cluster, as well as the nearest bubble to the wall, significantly influence the wall peak pressure. However, they have a minimal impact on the overall evolution of the bubble cluster and the peak pressure induced in the flow field. Remarkably, the spatial distribution of bubbles and the total number of bubbles play a crucial role in shaping the dynamic behavior of the bubble cluster and the pressure loads exerted both on the solid wall and in the flow field. The crucial findings offer profound insights into a range of applications, including cavitation erosion, underwater explosions, and drug delivery.

Deep smoothness weighted essentially non-oscillatory method for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators

Deep smoothness weighted essentially non-oscillatory method for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators

Analysis of spectral properties of WENO schemes in smooth regions

Weighted essentially non-oscillatory (WENO) schemes are a class of numerical schemes designed for solving problems with discontinuities. The spectral properties of them are hard to analyze because of their nonlinearities. A method of analyzing the average scheme in effect is proposed, by which we found that WENO schemes with a special kind of smoothness indicators can even obtain better spectral properties than their underlying linear schemes. This facilitates the design of WENO schemes with good spectral properties. The formulas of these smoothness indicators on sub-stencils have the same form except for different subscripts, which makes the nonlinear weights slightly close to the mean value. With this weight distribution, the resultant schemes behave like optimized upwind schemes with low dissipation and optimized dispersion properties. However, these WENO schemes may suffer from anti-dissipation and accuracy order degradation. Hence, they are suggested to be combined with the mapped WENO or the Z-type WENO methodology to address these problems. Some WENO schemes are taken as examples to illustrate the proposed methodology, and the results are in good agreement with those from the approximated dispersion relation (ADR) method.

Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem

AbstractTwo‐dimensional, nonlinear diffusion‐limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind‐biased and even‐centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essentially non‐oscillatory (WENO) flux schemes, along with variations and hybrids of these. All schemes were coupled with comparably high order even‐centred Lagrangian interpolations and pressure gradient/divergence approximations, and O18 spatial filtering. Subgrid‐scale (SGS) turbulent flux calculations, with a constant eddy‐mixing coefficient, were made with O2 spatial approximations (O4–20 accurate SGS turbulent fluxes had little impact). Using a range of resolutions from Δx = Δz = 25–166.66… m for all schemes comparisons against an O17 flux, 25 m resolution reference solution showed solutions made with ≥O9 fluxes produced (often substantially) improved solutions, both visually and usually objectively, compared to solutions produced with lower order (<O9/10) fluxes, especially at intermediate resolutions (33.33–100 m). Expectedly, odd order solutions were increasingly damped as accuracy was decreased, especially from O9 to O3, especially for WENO solutions, while even order solutions were increasingly contaminated with dispersion and aliasing errors as accuracy was decreased, especially from O10 to O4. Odd order schemes also produced better solutions than even order schemes for <O9/10 fluxes, while the highest order (≥O13/14) schemes produced the best solutions, for any given resolution. Even order flux and Crowley flux (WENO) solutions were the least (most) computationally expensive, based on either floating‐point operations (FPO) or CPU times. Efficient WENO‐Sine and proposed hybrid Crowley‐WENO(‐Sine) schemes required fewer FPOs to produce more accurate solutions than traditional WENO schemes. We are encouraged by the often much improved visual and objective accuracy of very high order (≥O9) fluxes in simulations of a complex problem, and encourage further testing in numerical weather prediction models.

Multidimensional WENO-AO Reconstructions Using a Simplified Smoothness Indicator and Applications to Conservation Laws

Finite volume, weighted essentially non-oscillatory (WENO) schemes require the computation of a smoothness indicator. This can be expensive, especially in multiple space dimensions. We consider the use of the simple smoothness indicator sigma ^{textrm{S}}= frac{1}{N_{textrm{S}}-1}sum _{j} ({bar{u}}_{j} - {bar{u}}_{m})^2, where N_{textrm{S}} is the number of mesh elements in the stencil, {bar{u}}_j is the local function average over mesh element j, and index m gives the target element. Reconstructions utilizing standard WENO weighting fail with this smoothness indicator. We develop a modification of WENO-Z weighting that gives a reliable and accurate reconstruction of adaptive order, which we denote as SWENOZ-AO. We prove that it attains the order of accuracy of the large stencil polynomial approximation when the solution is smooth, and drops to the order of the small stencil polynomial approximations when there is a jump discontinuity in the solution. Numerical examples in one and two space dimensions on general meshes verify the approximation properties of the reconstruction. They also show it to be about 10 times faster in two space dimensions than reconstructions using the classic smoothness indicator. The new reconstruction is applied to define finite volume schemes to approximate the solution of hyperbolic conservation laws. Numerical tests show results of the same quality as standard WENO schemes using the classic smoothness indicator, but with an overall speedup in the computation time of about 3.5–5 times in 2D tests. Moreover, the computational efficiency (CPU time versus error) is noticeably improved.

Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-conservative Products

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of comparable accuracy. This makes them quite attractive for several science and engineering applications. But, to the best of our knowledge, such schemes have not been extended to non-linear hyperbolic systems with non-conservative products. In this paper, we perform such an extension which improves the domain of applicability of such schemes. The extension is carried out by writing the scheme in fluctuation form. We use the HLLI Riemann solver of Dumbser and Balsara (2016) as a building block for carrying out this extension. Because of the use of an HLL building block, the resulting scheme has a proper supersonic limit. The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme, thus expanding its domain of applicability. Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions, making it very easy for users to transition over to the present formulation. For conservation laws, the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO, with two major advantages:- 1) It can capture jumps in stationary linearly degenerate wave families exactly. 2) It only requires the reconstruction to be applied once. Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of accuracy for smooth multidimensional flows. Stringent Riemann ... *Abstract truncated, see PDF*

A new high order hybrid WENO scheme for hyperbolic conservation laws

AbstractThis article proposes an improved hybrid weighted essentially non‐oscillatory (WENO) scheme based on the third‐ and fifth‐order finite‐difference modified WENO (MWENO) schemes developed by Zhu et al. in (SIAM J. Sci. Comput. 39 (2017), A1089–A1113.) for solving hyperbolic conservation laws. The MWENO schemes give a guideline on whether to use the WENO scheme or the linear upwind scheme. Unfortunately, because there is no explicit formula for computing the roots of algebraic polynomials of order four or higher, it is difficult to generalize this criterion to higher order cases. Therefore, this article proposes a simple criterion for constructing a series of seventh‐, ninth‐, and higher‐order hybrid WENO schemes, and then designs a class of improved smooth indicator WENO (WENO‐MS) schemes. Compared with the classical WENO schemes, the main advantages of the WENO‐MS schemes are their robustness and efficiency. And these WENO‐MS schemes are more efficient, have better resolution, and can solve many extreme problems without any additional techniques. Furthermore, a simplification criterion is proposed to further improve the computational efficiency of the WENO‐MS schemes, and these simple WENO‐MS schemes are abbreviated as WENO‐SMS schemes in this article. Extensive numerical results demonstrate the good performance of the WENO‐MS schemes and the WENO‐SMS schemes.

A new family of downwind-limited, scale-invariant WENO schemes with optimal accuracy

Despite improvement over decades, there are still at least two key issues not fully solved in Weighted Essentially Non-oscillatory (WENO) schemes. Firstly, most WENO schemes hardly satisfy the scale-invariant property, which undermines their robustness and accuracy when simulating flows involving different scales such as reactive multi-component flows and plasma. Secondly, most of existing Essentially Non-oscillatory (ENO) constraints are not sufficient and necessary conditions to achieve optimal accuracy. Therefore, in this work, we design a new family of WENO schemes based on a three-cell stencil to address these two issues. The new WENO non-linear weights are designed as bounded asymptotic functions which are dependent on cell Normalised Volume Integrated Average (NVIA) values and a shape parameter θ. Thus, the new WENO weighting functions are scale-independent. The shape parameter θ controls the errors between the nonlinear weight and the ideal weight. As the value of θ increases, the new weighting functions become more accurate but also become more likely to produce numerical oscillations. Thus, we propose a downwind limiting method as a supplementary constraint of ENO property. The maximum value of θ which corresponds to the optimal accuracy of a weighting function can then be determined. The accuracy analysis via the standard Taylor expansion at critical points reveals that the proposed weighting functions outperform classical WENO schemes. The accuracy, scale-invariant property and ENO property of proposed schemes are further validated through benchmark tests, which shows the superior performance of the new schemes in comparison with existing three-cell-based WENO schemes. Thus, this work proposes a new direction to construct scale-invariant WENO weighting functions with optimal accuracy, which can potentially be extended to higher-order WENO schemes.

An improved discontinuity sensor for high-order weighted essentially non-oscillatory scheme on triangular meshes

In this paper, a new type of hybrid weighted essentially non-oscillatory (WENO) schemes with third-order and fourth-order accuracy is developed to simulate compressible flow problems on unstructured meshes. First, an improved discontinuity sensor is designed on unstructured meshes, which can automatically and accurately identify the troubled cells without manually adjusting the parameters related to the problem. Second, a hybrid unequal-sized WENO (US-WENO) scheme with different accuracy is developed based on the new hybridization strategy and the existing US-WENO scheme to reduce the computational overhead caused by the computation of nonlinear weights and local characteristic decompositions in WENO procedures. Finally, some benchmark examples are employed to verify the performance of the proposed method in terms of numerical dissipation, shock capture ability, and computational efficiency. Numerical experiments show that the proposed hybrid US-WENO schemes can inherit the excellent characteristics of the original US-WENO schemes while improving computational efficiency.

Three-dimensional high-order finite-volume method based on compact WENO reconstruction with hybrid unstructured grids

In the present work, a three-dimensional (3D) high-order finite-volume method, based on the compact simple weighted essentially non-oscillatory (WENO) reconstruction for hybrid unstructured grids, is developed. For each control cell, its stencils only involve neighboring cells. By ensuring that the various orders of the derivatives of the conservative variables are conserved over the stencils, an over-determined system of equations is formed, and the polynomials corresponding to each stencil are obtained by solving this system of equations using the least-squares method. The artificially determined weight coefficients, and the smoothing factors based on the smoothness of the flow field, are used to determine the nonlinear weights, which nonlinearly combine the polynomials of each stencil to obtain the final high-order reconstruction polynomial. Consequently, the conservative variables on the interface can be interpolated and the sphere-function based discrete gas-kinetic scheme (DGKS) is used to locally solve the Boltzmann equation. Lastly, the fluxes are calculated using the mesoscopic perspective based on the moment relations. The present algorithm has the following advantages: the stencils only involve the neighboring cells of each control volume, making the algorithm compact and simpler, especially for the operation of the boundary cells; the unknown coefficients are solved by the least-squares method to avoid the coefficient matrix being ill-conditioned; the simple WENO scheme artificially chooses the value to guarantee positive weights, in addition, the algorithm can be applied to 3D hybrid unstructured grids, making it more adaptable. In terms of flux calculation, DGKS not only inherits the advantages of the traditional gas-kinetic schemes (GKS) but also greatly simplifies the flux calculation expressions. Several cases are simulated to verify the correctness and robustness of the algorithm, and the accuracy test shows the algorithm is third-order accurate.

A New Entropy Stable Finite Difference Scheme for Hyperbolic Systems of Conservation Laws

The hyperbolic problem has a unique entropy solution, which maintains the entropy inequality. As such, people hope that the numerical results should maintain the discrete entropy inequalities accordingly. In view of this, people tend to construct entropy stable (ES) schemes. However, traditional numerical schemes cannot directly maintain discrete entropy inequalities. To address this, we here construct an ES finite difference scheme for the nonlinear hyperbolic systems of conservation laws. The proposed scheme can not only maintain the discrete entropy inequality, but also enjoy high-order accuracy. Firstly, we construct the second-order accurate semi-discrete entropy conservative (EC) schemes and ensure that the schemes meet the entropy identity when an entropy pair is given. Then, the second-order EC schemes are used as a building block to achieve the high-order accurate semi-discrete EC schemes. Thirdly, we add a dissipation term to the above schemes to obtain the high-order ES schemes. The term is based on the Weighted Essentially Non-Oscillatory (WENO) reconstruction. Finally, we integrate the scheme using the third-order Runge–Kutta (RK) approach in time. In the end, plentiful one- and two-dimensional examples are implemented to validate the capability of the scheme. In summary, the current scheme has sharp discontinuity transitions and keeps the genuine high-order accuracy for smooth solutions. Compared to the standard WENO schemes, the current scheme can achieve higher resolution.

An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed the widely concerned issue of the previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is rather difficult to achieve high resolutions on the premise of removing spurious oscillations for long-run simulations of the hyperbolic systems. In the present study, we extend the OP criterion to the WENO-Z-type schemes as the forementioned issue has also been extensively observed numerically for these schemes. Firstly, we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Z-type weights in a uniform formula from the perspective of the mapping relation. Then, we naturally introduce the OP criterion to improve the WENO-Z-type schemes, and the resultant schemes are denoted as MOP-GMWENO-X. Finally, extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes. We draw the conclusion that, the convergence propoties of the proposed schemes are equivalent to the corresponding WENO-X schemes. The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations. The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.

A new type of improved third order WENO scheme with finite difference framework

In this paper, we present a novel variety of third order finite difference weighted essentially non-oscillatory (WENO) scheme based on WENO-ZQ scheme to approximate the computational solutions of one- and two-dimensional non-linear hyperbolic conservation laws. The new reconstruction process of fluxes is the convex combination of a second degree polynomial and two linear polynomials. We apply a new modified global smoothness indicator into the non-linear weights. We also use the power parameter ‘p’ to balance the accuracy of the proposed scheme. This novel third order WENO scheme applies three points data {xi−1,xi,xi+1} same as WENO-JS3 and WENO-Z3 schemes. In the proposed scheme, the main advantages are that the associated linear weights can be taken as any positive numbers on condition their summation is one. Also, it is easy to be used in multi-dimensional engineering problems. We implement the time discretization by using third order accurate strong stability preserving Runge–Kutta method. The extensive computational experiments of a collection of benchmark test problems are provided to demonstrate high resolution, robustness and absolute truncation errors in L1 and L∞ norms. We observe from the results that the new scheme contains better capability in performance than WENO-PZ3 scheme.

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic Mach number ε ranging from 0 to O(1). High-order accuracy in time is obtained by SI implicit-explicit Runge–Kutta (IMEX-RK) time discretization. High-order accuracy in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions. A constrained transport method is applied to maintain a discrete divergence-free condition. We formally prove that the scheme is AP. Asymptotic accuracy (AA) in the incompressible MHD limit is obtained if the implicit part of the SI IMEX-RK scheme is stiffly accurate. Numerical experiments are provided to validate the AP, AA, and divergence-free properties of our proposed approach. Besides, the scheme can well capture discontinuities such as shocks in an essentially non-oscillatory fashion in the compressible regime, while it is also a good incompressible solver with uniform large-time step conditions in the low sonic Mach limit.

A sixth-order central WENO scheme for nonlinear degenerate parabolic equations

In this paper, we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for the WENO reconstruction to avoid the negative linear weights. We choose the Z-type nonlinear weights based on the $$L^2$$ -norm smoothness indicators, yielding the new WENO scheme with less computational cost. It is also confirmed that the proposed central WENO scheme with the devised nonlinear weights achieves sixth order accuracy in smooth regions. One- and two-dimensional numerical examples are presented to demonstrate the improved performance of the proposed central WENO scheme.

A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations

To improve the shock-capturing capability of the third-order WENO scheme and enhance its computational efficiency, in this paper, we design a new WENO scheme independent of the local smoothing factor, WENO-SIF. The weight function of the WENO-SIF scheme is the segmentation function of the sub-stencil, which is guaranteed to achieve the desired accuracy at higher order critical points. WENO-SIF does not need to compute the smoothing factor during the computation, which effectively reduces the computational consumption. The present WENO-SIF is compared with WENO-JS and other WENO schemes for numerical experiments at one- and two-dimensional benchmark problems with a suitable choice of $$\lambda =0.13$$ . The results demonstrate that the WENO scheme can further improve the resolution of WENO-JS, achieve optimal accuracy at high-order critical points, and significantly reduce the computational consumption.

High-Order WENO-based Semi-Implicit Projection Method for Incompressible Turbulent Flows: Development, Accuracy, and Reynolds Number Effects

A novel high-order projection method is presented in this study for the simulation of incompressible turbulent flows, utilising weighted essentially non-oscillatory (WENO) schemes. Spatial discretization involves using WENO schemes for nonlinear convection and standard central differences (CD) for the viscous term. The approach combines various orders of WENO and central difference schemes (WENO3/CD2, WENO5/CD4, and WENO7/CD6) to achieve third, fifth, and seventh-order spatial accuracy for velocity fields, respectively. Validating this method involved a thorough examination using the 2D Taylor Green vortex problem in both space and time, along with simulations of 3D Taylor-Green vortex problems at increasing Reynolds numbers (Re) of 1, 600, 16, 000, and 160, 000. The outcomes encompassed analyses of kinetic energy, enstrophy, energy spectra, and vortex fields, indicating the method's effectiveness in accurately simulating high Reynolds number turbulent flows without additional sub-grid scale models.

A high-robustness hybrid scheme of finite-difference WENO-THINC for compressible multicomponent flow scheme on general curvilinear grids

In this study, a high-robustness hybrid scheme of weighted essentially non-oscillatory (WENO) scheme with a modified tangent of hyperbola for interface capturing (THINC) algorithm is developed for compressible multicomponent flow on general curvilinear grids. Numerical errors induced by mesh deformation bring loss of numerical accuracy and simulation instability, resulting in inaccurate results such as interface distortion, numerical oscillations or even simulation failure. To address this issue, the WENO scheme combined with an improved THINC strategy is designed to alleviate these errors and maintain the high resolution of interfaces. A modified THINC algorithm is developed for the non-uniform grids, in which the steepness parameter is scaled adaptively according to varying grid spacings. This approach is capable of reducing numerical dissipations for interface reconstruction. The overestimated quasi-conservative WENO formulation are employed to hold the equilibriums of velocity, pressure, and temperature at the material interface. Numerical validations are tested on non-uniform grids with various randomness amplitudes to verify the effectiveness in one- and two-dimensional benchmark problems showing the better performances in shock- and interface-capturing capabilities.

A unified framework for non-linear reconstruction schemes in a compact stencil. Part 1: Beyond second order

Discretization of the convection term in a three-cell compact stencil has been widely used in Computational Fluid Dynamics (CFD) of engineering because the second-order interpolation scheme is considered to be more robust and algorithmically simple than very high-order schemes. However, according to Godnunov's theorem, it has never been trivial to design an accurate and oscillation-free discretization scheme in a compact stencil. Over decades, various kinds of schemes have been proposed to increase accuracy beyond second-order without producing non-physical numerical oscillations. Representative schemes are polynomial-based non-linear interpolations such as TVD (Total Variation Diminishing), NVD (Normalized Variable Diagram) and third-order WENO (Weighted Essentially Non-oscillatory); and non-polynomial-based interpolations including RBF (Radial Basis Functions), LDLR (Local Double Logarithmic Reconstruction) and Tangent of Hyperbola for INterface Capturing (THINC). Within the semi-discretization finite volume method, existing reconstruction schemes suffer from different issues to some extent. For example, existing TVD schemes tend to cause smearing, clipping and squaring effects. Most WENO schemes and inconsistent RBF schemes are not scale-invariant. Especially, the improved WENO-Z scheme is neither scale-invariant nor mesh-size-independent. Computationally expensive non-polynomial-based interpolations usually have singularity and are dependent on tunable parameters. Thus, this work reviews reconstruction schemes by reformulating or calculating the reconstructed boundary value in the normalised-variable space where the characteristics of reconstruction schemes can be read directly. Through the accuracy analysis and the induction of existing schemes, this work proposes a Unified Normalised-variable Diagram (UND) where the following properties of a reconstruction scheme can be given diagrammatically: 1) the second-order and the third-order accuracy condition, 2) the TVD and CBC (Convection Boundedness Criterion) constrain, 3) the ENO condition, 4) the High Resolution (HR) property, 5) and the numerical dissipation and anti-dissipation error.The proposed UND framework is firstly demonstrated by the improvement of the existing schemes with a shape-preserving TVD limiter and a scale-invariant WENO scheme. Then, by defining the normalised reconstruction operator, a brand-new scheme named ROUND (Reconstruction Operator on Unified Normalised-variable Diagram) is proposed. The ROUND scheme is devised by directly configuring the normalised reconstruction operator of favourable properties on UND. This work presents a dissipative ROUND scheme in which normalised reconstruction operators are fully in the dissipative region of UND, and a low-dissipative ROUND scheme where rigorously adjusted anti-dissipation errors are introduced. Different formulations of ROUND schemes are presented to show the flexibility of designing schemes within the UND framework. The proposed dissipative and low-dissipative ROUND schemes are evaluated via benchmark tests which show the superior performance of ROUND on accuracy and resolution. Especially, in some cases, the low-dissipative ROUND schemes obtain comparable and even better resolution than classic fifth-order WENO. The significance of this work is further demonstrated by the preliminary results of applying ROUND on the FDM-IBM (Finite Difference Method and Immersed Boundary Method) framework.

An efficient finite difference IFWENO-THINC hybrid scheme for capturing discontinuities

The weighted essentially non-oscillatory (WENO) scheme is a famous shock-capturing scheme, but for high-precision numerical simulation, the classical WENO scheme is always considered to have excessive dissipation and insufficient resolution near discontinuities. Improving the accuracy order or reducing the dissipation of the WENO by optimizing the linear weights can effectively improve the resolution of this scheme in the smooth regions. However, under the same method, the improvement of shock-capturing abilities is generally limited and may lead to numerical oscillations. In order to simultaneously improve the resolution in discontinuous regions and ensure the performance of the smooth regions, this study uses the shock detector to combine the tangent of hyperbola for interface capturing (THINC) scheme, which is a better discontinuity-capturing scheme, with a given WENO discretization, such as the improved fast WENO (IFWENO) scheme that equips with high economy and does not loss accuracy at any critical point. The hybrid method in this study is an apriori algorithm, which is more efficient and universal than the method in (Takagi et al. J. Comput. Phys. 452(2022)110899). Additionally, the performance of the THINC scheme in different regions near the discontinuity is analyzed in detail through numerical experiments, and a shock detector that can fully exploit the advantages of the THINC scheme is provided. By using this shock detector, several one-dimensional and two-dimensional numerical cases are employed to verify that the hybrid scheme can greatly improve the performance in discontinuities without affecting the flow structure in the smooth regions, which proves the effectiveness of the proposed shock detector and the excellence of the hybrid IFWENO-THINC scheme.