Spurious Numerical Oscillations Research Articles

Asymptotic preserving semi-Lagrangian discontinuous Galerkin methods for multiscale kinetic transport equations

We propose a new family of asymptotic preserving (AP) discontinuous Galerkin (DG) schemes for kinetic transport equations under a diffusive scaling. They are built upon a characteristics-based model reformulation proposed in Zhang et al. (2023) [27]. The reformulated model comprises a convection-diffusion-like equation for the macroscopic density and another evolution equation for the distribution function. We employ the equations in a weak form to enjoy the advantages of a DG method. We also leverage a semi-Lagrangian (SL) approach to achieve higher efficiency than a fully implicit scheme without loss of unconditional stability. A damping technique is introduced to control spurious numerical oscillations for high-order DG methods. We establish formal AP and Fourier stability analyses for fully discrete schemes in a linear scenario. Numerical experiments, covering one-dimensional to three-dimensional in space problems, confirm the accuracy, AP property, uniformly unconditional stability, and high parallel efficiency of the proposed methods.

A Comparative Analysis of Transient Finite-Strain Coupled Diffusion-Deformation Theories for Hydrogels

AbstractThis work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, general mathematical classification of the governing equations, and numerical implementation issues based on the finite element method. The theories are presented in a unified framework demonstrating that, despite not being evident in some cases, all of them follow equivalent thermodynamic arguments. A detailed computational analysis is carried out where Taylor–Hood elements are employed in the spatial discretization to satisfy the inf-sup condition and to prevent spurious numerical oscillations. The resulting discrete problems are solved using the FEniCS platform through consistent variational formulations, employing both monolithic and staggered approaches. We conduct benchmark tests on various hydrogel structures, demonstrating that major differences arise from the chosen volumetric response of the hydrogel. The significance of this choice is frequently underestimated in the state-of-the-art literature but has been shown to have substantial implications on the resulting hydrogel behavior.

A structure-preserving upwind DG scheme for a degenerate phase-field tumor model

In this work, we present a modification of the phase-field tumor growth model given in [1] that leads to bounded, more physically meaningful, volume fraction variables. In addition, we develop an upwind discontinuous Galerkin (DG) scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model. Finally, some computational tests in accordance with the theoretical results are introduced. In the first test, we compare our DG scheme with the finite element (FE) scheme related to the same time approximation. The DG scheme shows a well-behavior even for strong cross-diffusion effects in contrast with FE where numerical spurious oscillations appear. Moreover, the second test exhibits the behavior of the tumor-growth model under different choices of parameters and also of mobility and proliferation functions.

Study of a numerical integration method using the compact scheme for electromagnetic transient simulations

This paper proposes a one-stage and oscillation free numerical integration method using the compact scheme for electromagnetic transient simulations. Since the compact scheme becomes L-stable at a moment when a circuit suddenly changes to a stiff system, the method is capable of suppressing the spurious numerical oscillations. Moreover, the compact scheme, which is a one-stage method, does not produce spurious spikes due to nonlinear elements. The compact scheme is compared with the trapezoidal method, the two-stage diagonally implicit Runge-Kutta (2S-DIRK) and the trapezoidal method with the second order backward difference formula (TR-BDF2). It follows from the comparison that the compact scheme does not produce the spurious numerical oscillations and spikes.

A note on an algorithm studying the uniform controllability of a class of semidiscrete hyperbolic problems

We propose an algorithm based on the the technique introduced in [23]. The aim of the algorithm is to study, in a simple way, the approximation of the controls for a class of hyperbolic problems. It is well-known that, the finite-difference semi-discrete scheme for the approximation of controls can leads to high frequency numerical spurious oscillations which gives a loss of the uniform (with respect to the mesh-size) controllability property of the semidiscrete model. It is also known that an appropriate filtration of the high eigenfrequencies of the discrete initial data enable us to restore the uniform controllability property of the whole solution. But, the methods used to prove such results are very constructive and contains difficult and fine computations. As an example, which proves the effectiveness of our algorithm, we consider the case of the semidiscrete one dimensional wave equation. In this particular case, we are able to prove the uniform controllability, where the initial data are filtered in a range which contains as many modes as possibles, taking into account previous results obtained in literature (see [18]).

Explicit asynchronous time scheme with local push-forward stepping for discontinuous elastic wave propagation: One-dimensional heterogeneous cases and Hopkinson bar experiment

This is a presentation of robust and accurate explicit time-stepping strategy for finite element modeling of elastic discontinuous wave propagation in strongly heterogeneous, multi-material and graded one-dimensional media. One of the major issues in FEM modeling is the existence of spurious numerical stress oscillations close to theoretical wave fronts due to temporal-spatial dispersion behavior of FE discretization. The numerical strategy presented for modeling of 1D discontinuous elastic waves is based on (a) pushforward-pullback local stepping — ensuring the elimination of dispersion due to different critical time step sizes of finite elements, (b) domain decomposition via localized Lagrange multipliers — to satisfy coupling kinematics and dynamic equations , (c) asynchronous time scheme — ensuring the correct information transfer of quantities for the case of integer ratios of time step size for all domain pairs. Dispersion behaviors, existence of spurious stress oscillations, and sensitivity of the dispersion to time step size are then suppressed. The proposed method is numerically tested with regard to the rectangular step pulse elastic propagation problem considering in-space varying Young’s modulus. To prove robustness and accuracy, a comparison with results from commercial software, an analytical solution, and experimental data from partial assembly of a split Hopkinson pressure bar (SHPB) setup is provided.

High-order implicit RBF-based differential quadrature-finite volume method on unstructured grids: Application to inviscid and viscous compressible flows

This paper exploits the potential of a high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method for effective simulation of inviscid and viscous compressible flows using unstructured grids. The framework of IRBFDQ-FV method is based on finite volume discretization which can guarantee conservation of mass, momentum and energy. The flow field variables within each control cell are represented by a fourth-order approximation constructed by a Taylor series expansion to the cell center with spatial derivatives as the undetermined coefficients. All spatial derivatives are computed by the meshless and highly converged RBF-based differential quadrature (RBFDQ) technique. Regarding flux evaluation, the discrete gas-kinetic flux solver is applied to evaluate inviscid and viscous fluxes simultaneously for compressible viscous flows. Resultantly, the special mathematical treatment for the viscous flux, which is usually adopted in other high-order methods, can be avoided. A point extrema-based extended bounds (PEEB) shock-capturing limiter is introduced to eliminate spurious numerical oscillations near discontinuities. Due to the implicit nature of the proposed method, implicit time-stepping schemes compatible with the spatial accuracy are devised to efficiently solve the resulting discretized equations. Representative compressible flow problems are simulated to verify the high-order accuracy, excellent efficiency and robustness of the present method. Comparison with two other high-order finite volume methods further shows competitiveness of the present method in solving compressible flow problems on unstructured grids.

Deneb: An open-source high-performance multi-physical flow solver based on high-order DRM-DG method

High-order methods are being recognized as powerful tools for handling scale-resolving simulations over complex geometry. However, several obstacles still block their complete applications to practical engineering problems: a compromise between accuracy and efficiency on mixed-curved meshes, inherent vulnerability to numerical oscillations, and lack of open-source high-performance solvers for researchers. To address these issues, we present Deneb, an open-source high-order accurate numerical solver that enables high-performance scale-resolving simulations on PDE-based flow systems. Deneb uses the physical domain-based modal discontinuous Galerkin (DG) method; thus, it can provide an arbitrary high-order accurate solution on mixed-curved meshes and has the potential for handling polyhedral meshes as well. The direct reconstruction method (DRM) efficiently executes the numerical integration of DG volume and surface integrals without accuracy loss on non-affine elements where mapping functions are high-degree. The resulting DRM-DG method eliminates the severe cost of a quadrature-based approach on mixed-curved meshes. Deneb offers explicit and implicit Runge–Kutta methods as well to achieve high-order accuracy in time. In addition, Krylov subspace methods and preconditioners are available for high-performance linear system solving in parallel. Deneb possesses a strong capability to resolve multi-physical shocks without numerical instabilities with the aid of multi-dimensional limiting and artificial viscosity methods. In particular, the hierarchical multi-dimensional limiting process enables efficient computations of supersonic flows without time-step restriction. The current release of Deneb covers the simulations of hypersonic equilibrium and magneto-hydrodynamic flows as well as compressible Navier–Stokes equations, but it has the potential to solve any PDE-based multi-physical flow systems. Several benchmark problems are presented to highlight Deneb's capability to perform scale-resolving and multi-physical flow simulations. A scalability test is also presented to verify the scaling characteristics of Deneb for high-performance computing. Program summaryProgram title: DenebCPC library link to program files:https://doi.org/10.17632/723n5r797n.1Developer's repository link:https://github.com/HojunYouKr/DenebLicensing provisions: BSD-3-ClauseProgramming language: C++17Nature of problem: The physical domain-based modal DG method can achieve the expected order of accuracy with the optimal number of polynomial bases even on non-affine elements. However, the DG method becomes significantly expensive on high-order curved elements when using quadrature rules, blocking its applicability to practical engineering problems. The numerical integration should be much more efficient without compromising accuracy. In addition, the less diffusive nature of high-order methods makes them susceptible to producing spurious numerical oscillations near flow discontinuities, potentially leading to numerical instabilities. Thus, an accurate and robust shock-capturing method is essential to simulate multi-physical flows under compressible regimes. Finally, the solver needs high scalability to perform large-scale computations in parallel.Solution method: DRM is applied to the DG volume and surface integrals to perform efficient numerical integration on non-affine elements without accuracy loss. The resulting method, DRM-DG, provides arbitrary high-order accurate solutions to various PDE-based flow problems on mixed-curved meshes. The solution is also high-order accurate in time due to high-order explicit and implicit Runge–Kutta methods implemented. The external library enables high-performance linear system solving with various preconditioners in parallel. Both multi-dimensional limiting and artificial viscosity methods suppress unwanted subcell oscillations across physical discontinuities. In particular, the limiting methods simulate complex supersonic flows efficiently without time-step restriction. The solver is highly scalable on parallel computing with the aid of non-blocking communications and latency hiding.

A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows

We propose a high order finite difference linear scheme combined with a high order bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For such problem with highly oscillatory structure but not strong shocks, our approach seems to be less dissipative and much less costly than a WENO type scheme, and has high resolution due to a Hermite reconstruction. Spurious numerical oscillations can be controlled by the MPP flux limiter. Numerical tests are performed for the Vlasov-Poisson system, the 2D guiding-center model and the incompressible Euler system. The comparison between the linear and WENO type schemes will demonstrate the good performance of our proposed approach.

Transient Acoustic Wave Propagation Problems in Multilayered Pavement Using a Time Discontinuous Galerkin Finite Element Method

This paper presents a modified time discontinuous Galerkin finite element method (MDGFEM) for transient acoustic wave propagation problem of multilayered pavement. The pavement consists of cement concrete pavement, semi-rigid base, and natural soil. The multilayered pavement is modeled as poroelastic mediums and assumed to be water-saturated. The well-known generalized Biot’s theory is employed to describe the wave propagation problem. The present MDGFEM, based on the artificial damping scheme, employs the Hermite (P3) functions and the linear (P1) shape functions to interpolate the global nodal vector and its temporal gradient respectively in a time step. Numerical results of 1D and 2D problems show that the MDGFEM can filter out spurious numerical oscillations before and after waves, boundaries of the hole, and the interface between the layers more effectively for the propagation of acoustic waves in multilayered pavement. Compared with widely used time-continuous methods such as the Newmark method, the method proposed in this paper presents better capabilities in the fluid–structure interaction behavior of multilayer pavements and provides a more accurate solution, which contributes to the further development of non-destructive testing of multilayer pavement structures.

Improved fifth-order weighted essentially non-oscillatory scheme with low dissipation and high resolution for compressible flows

Compressible flows are numerically simulated using hyperbolic conservation laws. This study proposes a modified fifth-order weighted essentially non-oscillatory (WENO) scheme with a relatively low dissipation and high resolution for hyperbolic conservation laws. This scheme exhibits good performance when solving complex compressible flow fields containing strong discontinuities and smooth microstructures. A simple local smoothness indicator and an eighth-order global smoothness indicator are introduced to improve the accuracy. Furthermore, we construct a new optimal coefficient, which can be adaptively adjusted with different states of the flow field. It no longer depends on the grid spacing. This adaptive coefficient not only reduces dissipation while improving the resolution but also prevents negative dissipation and effectively suppresses spurious numerical oscillations. The proposed scheme attains a higher accuracy at high-order critical points than three classical WENO schemes. Moreover, analysis of the approximate dispersion relation indicates that the proposed scheme provides good dispersion and dissipation properties compared with other WENO schemes. Finally, several standard numerical experiments are performed to demonstrate the enhanced performance of the proposed scheme. The numerical results indicate that the present scheme has a low dissipation, high resolution, and good stability to capture both smooth and discontinuous structures.

Time-discontinuous state-based peridynamics for elasto-plastic dynamic fracture problems

A time-discontinuous state-based peridynamic method (SBPD-TD) is developed in this paper to model the transient problems of wave and crack propagation in solids. In this method, the non-local deformation gradient is derived in a consistent way using the least square method, so that the classical elasto-plastic constitutive relationship can be directly adopted in the SBPD based on the correspondence material modeling. Then the displacement field and the velocity field are interpolated independently in the temporal domain respectively, in which the jump terms representing the discontinuities of variables are introduced between the adjacent time steps. After that, an integral weak form in the temporal domain of the spatially discrete governing equations is constructed and the basic formula of SBPD-TD is derived. The above-mentioned characteristics ensure that the SBPD-TD can accurately capture the sharp gradient characteristics in the propagation of elastic and plastic stress waves and effectively control the spurious numerical oscillations. Several representative numerical examples show that the SBPD-TD provides more accurate and satisfactory results when compared with the conventional SBPD, and has broad applications to predict the contact impact fracture behaviors of various materials.

A class of finite element methods with averaging techniques for solving the three-dimensional drift-diffusion model in semiconductor device simulations

Obtaining a satisfactory numerical solution of the classical three-dimensional drift-diffusion (DD) model, widely used in semiconductor device simulations, is still challenging nowadays, especially when the convection dominates the diffusion. In this work, we propose a series of finite element schemes with different types of averaging techniques to discretize the three-dimensional continuity equations. Our methods are based on the classical finite element framework, quite different from those mixed finite element/volume methods that also employ inverse averaging techniques. At first, the Slotboom variables are employed to transform the continuity equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then four averaging techniques, denoted with A1-A4, are introduced to approximate the exponential coefficient with its average on every tetrahedral element of the grid. The first scheme calculates the harmonic average of the exponential coefficient on a whole tetrahedron, and the other three schemes calculate the average of the exponential coefficient on each edge of a tetrahedral element. Our methods can avoid the spurious non-physical numerical oscillations and guarantee the conservation of the computed terminal currents with a terminal current evaluation approach. In fact, these methods not only maintain numerical stability but also overcome the disadvantages of some stabilization methods that cannot guarantee the conservation of the terminal currents, such as the streamline-upwind Petrov-Galerkin (SUPG) method. Moreover, the derivation of these discretization methods does not need the dual Voronoi grid as that of the finite volume Scharfetter-Gummel (FVSG) method or other mixed finite element/volume methods with inverse averaging techniques, which greatly reduces the complexity of parallel implementations of our methods. Simulations on two realistic three-dimensional semiconductor devices are carried out to test the accuracy and stability of our methods. According to numerical results, we conclude that scheme A4 can produce more accurate numerical solutions than the other three schemes, especially when the bias applied on the electrode is high. Numerical results also show that the scheme A4 is more robust than the Zlámal finite element method [1] in high-bias cases, and it also performs better than the FVSG method and a tetrahedral mixed finite element method [2] on poor-quality grids. Scheme A4 is also employed to study rich physical properties of the n-channel MOSFET.

A Sequentially- Hybridized Locally Conservative Non-conforming Finite Element Scheme for Two-phase Flow Simulation through Heterogeneous Porous Media

Accurate two-phase flow modeling has a crucial role in detecting pollution in aquifers and/or in the simulating immiscible flow through porous media. In this research, a new hybrid numerical method based on the lower order non-conforming finite element method (NCFEM) and interior penalty discontinuous Galerkin (DG) method is proposed to simulate two-phase incompressible flow in heterogeneous porous media. The pressure and transport saturation equations are discretized by using the non-conforming Crouzeix-Raviart (CR) finite element and the symmetric weighed interior penalty discontinuous Galerkin (SWIPM). As a result of determining the degrees of freedom at the midpoint of neighboring element edges, a consistent set of pressure and velocity fields is obtained via the NCFEM. An H(div) projection based on the Raviart-Thomas (RT) element is implemented to improve the results resolution and preserve the continuity of the normal component of the velocity field. Besides, the spurious numerical oscillations of the saturation solution at the end of each time step are removed by using a novel vertex-based slope limiter, named the modified Chavent-Jaffre limiter. The accuracy and performance of the proposed numerical method are assessed by solving the Buckley-Leverett and McWhorter-Sunada benchmark problems, along with two test problems associated with highly heterogeneous porous media. The numerical results indicate that the proposed scheme has a remarkable potential to accurately capture the shock front and sharp interface zone of immiscible phases in the heterogeneous aquifers and other porous media.

Optimization of Lumped Parameter Models to Mitigate Numerical Oscillations in the Transient Responses of Short Transmission Lines

The Lumped Parameter Model (LPM) is a known approach to represent overhead transmission lines (TLs), especially when these elements comprehend a few tens of kilometers. LPMs employ a large number of cascaded π-circuits to compute accurately the transient responses. These responses contain numerical spurious oscillations (NSO) characterized by erroneous peaks which distort the transient responses, mainly their peak values. Two modified LPM topologies composed of damping resistances inserted along the longitudinal or transversal branches of the cascaded π-circuits offer significant mitigations in the NSO. In this paper, in an effort to have the maximum mitigation of the NSO and low distortion in the transient responses, two modified topologies with optimized damping resistances are proposed to represent short TLs. Results demonstrate expressive attenuation in the peaks of NSO which reflect good agreement in comparison with the responses computed by the Bergeron’s line model. The mitigation of the NSO is carried out directly in the time domain and it does not require either analog or digital filters.Furthermore, no frequency-to-time transformations are necessary in this procedure. These alternative topologies can be incorporated into any electromagnetic transient program to study switching operations in power systems.

Large-Eddy Simulation of Wind Turbine Flows: A New Evaluation of Actuator Disk Models

Large-eddy simulation (LES) with actuator models has become the state-of-the-art numerical tool to study the complex interaction between the atmospheric boundary layer (ABL) and wind turbines. In this paper, a new evaluation of actuator disk models (ADMs) for LES of wind turbine flows is presented. Several details of the implementation of such models are evaluated based on a test case studied experimentally. In contrast to other test cases used in previous similar studies, the present test case consists of a wind turbine immersed in a realistic turbulent boundary-layer flow, for which accurate data for the turbine, the flow, the thrust and the power are available. It is found that the projection of the forces generated by the turbine into the flow solver grid is crucial for rotor predictions, especially for the power, and less important for the wake flow prediction. In this context, the projection of the forces into the flow solver grid should be as accurate as possible, in order to conserve the consistency between the computed axial velocity and the projected axial force. Also, the projection of the force is found to be much more important in the rotor plane directions than in the streamwise direction. It is found that for the case of a wind turbine immersed in a realistic turbulent boundary-layer flow, the potential spurious numerical oscillations originating from sharp force projections are not harmful to the results. By comparing an advanced model which computes the non-uniform distribution of the turbine forces over the rotor with a simple model which assumes uniform effects of the turbine forces, it is found that both can lead to accurate results for the far wake flow and the thrust and power predictions. However, the comparison shows that the advanced model leads to better results for the near wake flow. In addition, it is found that the simple model overestimates the rotor velocity prediction in comparison to the advanced model. These elements are explained by the lack of local feedback between the axial velocity and the axial force in the simple model. By comparing simulations with and without including the effects of the nacelle and tower, it is found that the consideration of the nacelle and tower is relatively important both for the near wake and the power prediction, due to the shadow effects. The grid resolution is not found to be critical once a reasonable resolution is used, i.e., in the order of 10 grid points along each direction across the rotor. The comparison with the experimental data shows that an accurate prediction of the flow, thrust, and power is possible with a very reasonable computational cost. Overall, the results give important guidelines for the implementation of ADMs for LES.

Numerical simulation of impulse waves in Cosserat media based on a time‐discontinuous Galerkin finite element method

AbstractThe time‐discontinuous Galerkin finite element method (TDGFEM) has advantages in reducing spurious numerical oscillations and capturing discontinuities of solutions in space for high‐frequency dynamical problems. This article extends TDGFEM into Cosserat media to focus on impulse wave propagations, involving rotational wave and effects of microstructures. The Cosserat continuum theory contains additional rotational degrees of freedom, leading to Cosserat compressive (P), shear (S), and rotational (R) waves. Therefore, three Cosserat wave propagations are simulated by TDGFEM under impulse loads in this article. Different orders (P1–P3) of temporal shape functions are presented for Cosserat nodal unknown vectors, leading to different matrix equations for TDGFEM. One‐dimensional numerical results show capacity and efficiency of TDGFEM simulating Cosserat impulse wave propagations. Analyses about time step, mesh density and accuracy of TDGFEM are given in one‐dimensional examples. Results simulated by three methods with artificial damping are compared with those by TDGFEM, which shows a higher efficiency for TDGFEM. Two‐dimensional results present the propagation characteristics of Cosserat impulse P, S, and R waves, and velocities of Cosserat P, S, and R waves are simulated by TDGFEM. The characteristic length and Cosserat shear modulus have a major influence on impulse S and R wave propagations.

An actuator‐line model with Lagrangian‐averaged velocity sampling and piecewise projection for wind turbine simulations

AbstractA new approach is proposed to do the velocity sampling for actuator‐line models (ALM). Unlike the conventional spatial averaging approaches, the velocity sampling is performed in a Lagrangian averaging way along flow paths with a time scale depending on the local flow patterns. The new approach is evaluated by large‐eddy simulations of a utility‐scale National Renewable Energy Laboratory (NREL)‐5MW wind turbine. The results show that the Lagrangian approach of velocity sampling is effective to reduce the spurious numerical oscillations in the modeling results. The good match with the benchmark data indicates that correct free upwind velocity can be obtained with a careful determination of the associated time scale. Also, a piecewise function is proposed to replace the Gaussian function for the force projection process.

Hydraulic Transient Analysis of Sewer Pipe Systems Using a Non-Oscillatory Two-Component Pressure Approach

On the basis of the two-component pressure approach, we developed a numerical model to capture mixed transient flows in close conduit systems. To achieve this goal, an innovative Godunov finite-volume numerical scheme is proposed to suppress the spurious numerical oscillations occurring during rapid pipe pressurization. To dissipate the spurious numerical oscillations, we admit artificial numerical viscosity to the numerical scheme through applying a proposed Harten, Lax, and van Leer (HLL) Riemann solver for calculating the numerical fluxes at the computational cell interfaces. The proposed solver controls the magnitude of the numerical viscosity through adjusting the left and right wave velocities. A wave velocity calculator is proposed to optimally distribute the numerical viscosity over several computational cells around the computational cell in which the pressurization front is located. The proposed solver admits significant artificial numerical viscosity when the pipe pressurization is imminent and automatically reduces it in other places; in this way the numerical diffusion and data smearing is minimized. The validity of the proposed model is justified by the aid of several test cases in which the numerical results are compared with both experimental data and the results obtained from analytical methods. The results reveal that the proposed model succeeds in completely removing the spurious numerical oscillations, even when the pipe acoustic speed is over 1000 m/s. The numerical results also show that the model can successfully capture occurrence of negative pressures during the course of transient flow.

A Staggered Semi-implicit Discontinuous Galerkin Scheme with a Posteriori Subcell Finite Volume Limiter for the Euler Equations of Gasdynamics

In this paper we propose a novel semi-implicit Discontinuous Galerkin (DG) finite element scheme on staggered meshes with a posteriori subcell finite volume limiting for the one and two dimensional Euler equations of compressible gasdynamics. We therefore extend the strategy adopted by Dumbser and Casulli (Appl Math Comput 272:479–497, 2016), where the Euler equations have been solved solved using a semi-implicit finite volume scheme based on the flux-vector splitting method recently proposed by Toro and Vazquez-Cendon (Comput Fluids 70:1–12, 2012). In our scheme, the nonlinear convective terms are discretized explicitly, while the pressure terms are discretized implicitly. As a consequence, the time step is restricted only by a mild CFL condition based on the fluid velocity, which makes this method particularly suitable for simulations in the low Mach number regime. However, the conservative formulation of the scheme, together with the novel subcell finite volume limiter allows also the numerical simulation of high Mach number flows with shock waves. Inserting the discrete momentum equation into the discrete total energy conservation law yields a mildly nonlinear system with the scalar pressure as the only unknown. Due to the use of staggered meshes, the resulting pressure system has the most compact stencil possible and can be efficiently solved with modern iterative methods. In order to deal with shock waves or steep gradients, the new semi-implicit DG scheme proposed in this paper includes an a posteriori subcell finite volume limiting technique. This strategy was first proposed by Dumbser et al. (J Comput Phys 278:47–75, 2014) for explicit DG schemes on collocated grids and is based on the a posteriori MOOD algorithm of Clain, Loubere and Diot. Recently, this methodology was also extended to semi-implicit DG schemes on staggered meshes for the shallow water equations in Ioriatti and Dumbser (Appl Numer Math 135:443–480, 2019). Within the MOOD approach, an unlimited DG scheme first produces a so-called candidate solution for the next time level $$t^{n+1}$$. Later on, the control volumes with a non-admissible candidate solution are identified by using physical and numerical detection criteria, such as the positivity of the solution, the absence of floating point errors and the satisfaction of a relaxed discrete maximum principle (DMP). Then, in the detected troubled cells a more robust first order semi-implicit finite volume (FV) method is applied on a sub-grid composed of $$2P + 1$$ subcells, where P denotes the polynomial degree used in the DG scheme. For that purpose, the nonlinear convective terms are recomputed in the troubled cells using an explicit finite volume scheme on the subcell level. Also the linear system for the pressure needs to be assembled and solved again, but where now a low order semi-implicit finite volume scheme is used on the sub-cell level in all troubled DG elements, instead of the original high order DG method. Finally, the higher order DG polynomials are reconstructed from the piecewise constant subcell finite volume averages and the scheme proceeds to the next time step. In this paper we present, discuss and test this novel family of methods and simulate a set of classical numerical benchmark problems of compressible gasdynamics. Great attention is dedicated to 1D and 2D Riemann problems and we also show that for these test cases the scheme responds appropriately in the presence of shock waves and does not produce non-physical spurious numerical oscillations.