Convective Terms Research Articles

Discretisations of mixed-dimensional Thermo-Hydro-Mechanical models preserving energy estimates

In this study, we explore mixed-dimensional Thermo-Hydro-Mechanical (THM) models in fractured porous media accounting for Coulomb frictional contact at matrix fracture interfaces. The simulation of such models plays an important role in many applications such as hydraulic stimulation in deep geothermal systems and assessing induced seismic risks in CO2 storage. We first extend to the mixed-dimensional framework the thermodynamically consistent THM models derived in [19] based on first and second principles of thermodynamics. Two formulations of the energy equation will be considered based either on energy conservation or on the entropy balance, assuming a vanishing thermo-poro-elastic dissipation. Our focus is on space time discretisations preserving energy estimates for both types of formulations and for a general single phase fluid thermodynamical model. This is achieved by a Finite Volume discretisation of the non-isothermal flow based on coercive fluxes and a tailored discretisation of the non-conservative convective terms. It is combined with a mixed Finite Element formulation of the contact-mechanical model with face-wise constant Lagrange multipliers accounting for the surface tractions, which preserves the dissipative properties of the contact terms. The discretisations of both THM formulations are investigated and compared in terms of convergence, accuracy and robustness on 2D test cases. It includes a Discrete Fracture Matrix model with a convection dominated thermal regime, and either a weakly compressible liquid or a highly compressible gas thermodynamical model.

A new class of efficient high order semi-Lagrangian IMEX discontinuous Galerkin methods on staggered unstructured meshes

In this paper we present a new high order semi-implicit discontinuous-Galerkin (DG) scheme on two-dimensional staggered triangular meshes applied to different nonlinear systems of hyperbolic conservation laws such as advection-diffusion models, incompressible Navier-Stokes equations and natural convection problems. While the temperature and pressure field are defined on a triangular main grid, the velocity field is defined on a quadrilateral edge-based staggered mesh. A semi-implicit time discretization is proposed, which separates slow and fast time scales by treating them explicitly and implicitly, respectively. The nonlinear convection terms are evolved explicitly using a semi-Lagrangian approach, whereas we consider an implicit discretization for the diffusion terms and the pressure contribution. High-order of accuracy in time is achieved using a new flexible and general framework of IMplicit-EXplicit (IMEX) Runge-Kutta schemes specifically designed to operate with semi-Lagrangian methods. To improve the efficiency in the computation of the DG divergence operator and the mass matrix, we propose to approximate the numerical solution with a less regular polynomial space on the edge-based mesh, which is defined on two sub-triangles that split the staggered quadrilateral elements. This allows for a fast computation of the DG operators and matrices without any need to store them for each mesh element. Due to the implicit treatment of the fast scale terms, the resulting numerical scheme is unconditionally stable for the considered governing equations because the semi-Lagrangian approach is the only explicit discretization for convection terms that does not need any stability restriction on the maximum admissible time step. Contrarily to a genuinely space-time discontinuous-Galerkin scheme, the IMEX discretization permits to preserve the symmetry and the positive semi-definiteness of the arising linear system for the pressure that can be solved at the aid of an efficient matrix-free implementation of the conjugate gradient method. We present several convergence results, including nonlinear transport and density currents, up to third order of accuracy in both space and time.

Robust discontinuous Galerkin-based scheme for the fully-coupled nonlinear thermo-hydro-mechanical problem

Abstract We present and analyze a discontinuous Galerkin method for the numerical modeling of the nonlinear fully-coupled thermo-hydro-mechanic problem. We propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. We focus on the treatment of the nonlinear convective transport term in the energy conservation equation and we propose suitable stabilization techniques that make the scheme robust for advection-dominated regimes. The stability analysis of the problem and the convergence of the fixed-point linearization strategy are addressed theoretically under mild requirements on the problem data. A complete set of numerical simulations is presented in order to assess the convergence and robustness properties of the proposed method.

Structural, optical and heat transfer characteristics of rotating [MgO+ ZrO2/PEG-H2O]h Hybrid nanofluid flow over an expanding surfaces with activation energy

SignificanceHybrid nanofluids have garnered significant interest due to their potential for enhanced thermal and optical properties compared to their individual counterparts. AimThe aim of this research is to examine the structural, optical, and heat transfer properties of a hybrid nanofluid [MgO+ZrO2/PEG-H2O]h within a rotating system. This research integrated variable viscosity, MHD, convection, and activation energy terms into the momentum, energy, and concentration equations. A comprehensive experimental analysis, including Fourier-transform infrared and ultraviolet visible spectroscopy, elucidates the structural arrangement, optical behavior, and thermal transport properties of the nanofluids. MethodologyThe partial differential equations that govern the system are converted into nonlinear ordinary differential equations through similarity transformations. Then, these ODEs are numerically solved by employing the Runge-Kutta-Fehlberg method in combination with a shooting procedure. FindingsThe research findings demonstrate that the rotational factor impacts skin friction differently by 2 % on x and y axes, while skin friction surges by 3.63 % in [MgO+ZrO2/PEG-H2O]h hybrid nanofluid with higher magnetic field intensity. The heat transmission rates of the [MgO+ZrO2/PEG-H2O]h hybrid nanofluid are significantly higher by 4.58 % compared to the [ZrO2/PEG-H2O]n nanofluid. The mass transfer rate of [ZrO2/PEG-H2O]n declines by 3.57 % with the rise of the activation energy factor. Utilizing spin coating, thin films of nanostructures [ZrO2/PEG-H2O]n, [MgO/PEG-H2O]n and [MgO+ZrO2/PEG-H2O]h are fabricated, resulting in films with a consistent thickness of ∼200 nm at a temperature of 25 °C. A reduction in the difference in energy bandgap values from 4.5 eV for [ZrO2/PEG-H2O]s to 5.3 eV for [MgO/PEG-H2O]n and 4.8 eV for [MgO+ZrO2/PEG-H2O]h is observed. This indicates that the [MgO+ZrO2/PEG-H2O]h hybrid nanofluid yields an appropriate bandgap compared to individual nanofluids because hybrid nanofluids can lead to synergistic mechanisms that elevate their electronic attributes.

Inconsistencies in unstructured geometric volume-of-fluid methods for two-phase flows with high density ratios

Geometric flux-based Volume-of-Fluid (VOF) methods (Marić et al., 2020) are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible single-field Navier–Stokes equations without phase-change (Liu et al., 2023), discretization may easily introduce inconsistencies that result in very large errors or catastrophic failure. We apply the consistency conditions derived for the ρLENT unstructured Level Set/Front Tracking method (Liu et al., 2023) to flux-based geometric VOF methods (Marić et al., 2020), and implement our discretization into the plicRDF-isoAdvector geometrical VOF method (Roenby et al., 2016). We find that computing the mass flux by scaling the geometrically computed fluxed phase-specific volume can ensure equivalence between the mass conservation equation and the phase indicator (volume conservation) if consistent discretization schemes are chosen for the temporal and convective term. Based on the analysis of discretization errors, we suggest a consistent combination of the temporal discretization scheme and the interpolation scheme for the momentum convection term. We confirm the consistency by solving an auxiliary mass conservation equation with a geometrical calculation of the face-centered density (Liu et al., 2023). We prove the equivalence between these two approaches mathematically and verify and validate their numerical stability for density ratios within [1, 106] and viscosity ratios within [102, 105].

A chemistry load balancing model for OpenFOAM

Efficient simulation tools are crucial for studying complex systems such as reacting flows where computational costs of computing chemical reaction rates can vastly exceed the costs for the integration of the convective and diffusive transport terms. Load imbalance in parallel computing poses a significant challenge for massively parallel reacting flow simulations. In response, a novel load balancing library has been developed to enhance OpenFOAM's solver performance in parallel environments. This library seamlessly integrates with OpenFOAM, offering ease of use and applicability to any OpenFOAM reacting solver incorporating finite-rate chemistry. In addition, it supports the standard and the dynamic adaptive chemistry model (TDAC) of OpenFOAM.The newly developed load-balanced standard and TDAC models address significant load imbalances by exchanging information between processes via MPI calls and tracking ODE solution times on a cell level. The TDAC model introduces dual tables on each core and enables immediate addition of computed solutions, enhancing computational efficiency. Validation on various test cases, including simulations on the HLRS Hawk supercomputer with up to 8000 cores, confirms identical results compared to the original unbalanced models, with notable speed-up factors of up to 6 for the standard and 5 for the TDAC model. Despite non-linear scaling at lower cell count per processor, load-balanced models consistently outperform unbalanced counterparts, making them the preferred choice for reacting flow simulations in OpenFOAM.

A Structure-Preserving Semi-implicit IMEX Finite Volume Scheme for Ideal Magnetohydrodynamics at all Mach and Alfvén Numbers

We present a divergence-free semi-implicit finite volume scheme for the simulation of the ideal magnetohydrodynamics (MHD) equations which is stable for large time steps controlled by the local transport speed at all Mach and Alfvén numbers. An operator splitting technique allows to treat the convective terms explicitly while the hydrodynamic pressure and the magnetic field contributions are integrated implicitly, yielding two decoupled linear implicit systems. The linearity of the implicit part is achieved by means of a semi-implicit time linearization. This structure is favorable as second-order accuracy in time can be achieved relying on the class of semi-implicit IMplicit–EXplicit Runge–Kutta (IMEX-RK) methods. In space, implicit cell-centered finite difference operators are designed to discretely preserve the divergence-free property of the magnetic field on three-dimensional Cartesian meshes. The new scheme is also particularly well suited for low Mach number flows and for the incompressible limit of the MHD equations, since no explicit numerical dissipation is added to the implicit contribution and the time step is scale independent. Likewise, highly magnetized flows can benefit from the implicit treatment of the magnetic fluxes, hence improving the computational efficiency of the novel method. The convective terms undergo a shock-capturing second order finite volume discretization to guarantee the effectiveness of the proposed method even for high Mach number flows. The new scheme is benchmarked against a series of test cases for the ideal MHD equations addressing different acoustic and Alfvén Mach number regimes where the performance and the stability of the new scheme is assessed.

Existence and regularity results of parabolic problems with convection term and singular nonlinearity

In this work, we investigate the influence of the convection term and the singular lower order term on the existence and regularity of solutions to the following parabolic problem: \begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}(M(x,t)\nabla u) =-\operatorname{div}(uE(x,t))+\frac{f}{u^{\theta}}&\text{in }\Omega\times(0,T),\\ u(x,t)=0&\text{on }\partial \Omega\times (0,T),\\ u(x,0)=u_{0}(x)&\text{in }\Omega,\end{cases} where \theta>0 , \Omega\subset \mathbb{R}^{N}\ (N>2) is a bounded smooth domain with 0\in \Omega , and f\in L^{m}(\Omega\times (0,T)) with m\geq 1 is a non-negative function. The function u_{0} is a non-negative function that belongs to the space L^{\infty}(\Omega) such that \forall \omega\subset\subset \Omega,\ \exists c_{\omega}>0,\quad u_{0}\geq c_{\omega}\text{ in }\omega. The main idea of this research explains the combined impact of the convection term and the singular lower order term on the existence and regularity of a solution to the above problem.

On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations

Abstract In this paper, we propose and analyze a discontinuous Galerkin finite element method for solving the transient Boussinesq incompressible heat conducting fluid flow equations. This method utilizes an upwind approach to handle the nonlinear convective terms effectively. We discuss new a priori bounds for the semidiscrete discontinuous Galerkin approximations. Furthermore, we establish optimal a priori error estimates for the semidiscrete discontinuous Galerkin velocity approximation in L 2 \mathbf{L}^{2} and energy norms, the temperature approximation in L 2 L^{2} and energy norms and pressure approximation in L 2 L^{2} -norm for t > 0 t>0 . Additionally, under the smallness assumption on the data, we prove uniform in time error estimates. We also consider a backward Euler scheme for full discretization and derive fully discrete error estimates. Finally, we provide numerical examples to support the theoretical conclusions.

LES of Premixed Turbulent Combustion Using Filtered Tabulated Chemistry

AbstractThe filtered tabulated chemistry (FTACLES) approach utilizes data from pre-tabulated explicitly filtered 1D flame profiles for closure of the LES-filtered transport terms. Different methodologies are discussed to obtain a suitable progress variable c from detailed chemistry calculations of a methane/air flame. In this context, special focus is placed on the analytical modeling of the reaction source term using series of parameterized Gaussians. For increasing effective filter sizes in LES (i.e. including the flame thickening) the precise shape of the reaction rate profile becomes less and less relevant. In particular, it is shown that for one-step chemistry, a single Gaussian is sufficient to derive an explicitly expressible 1D flame profile with a prescribed laminar flame speed and thermal flame thickness. The resulting artificial flame profile is shown to have similarities with profiles based on carbon chemistry and detailed reaction mechanisms. Next, the behavior of the filtered c-transport equation is analyzed and several possible closure methods are compared for a wide range of filter widths. It is shown that the unclosed contribution of the filtered diffusion term can be combined with the subgrid convection term, thus simplifying the FTACLES formulation. The model is implemented in OpenFOAM and validated in 1D for a variety of LES filter sizes in combination with artificial flame thickening. A power-law-based wrinkling model is modified for use with artificial flame thickening and combined with the FTACLES model to enable 3D simulations of a premixed turbulent Bunsen burner. The comparison of 3D Large Eddy Bunsen flame simulations at increasing levels of turbulence intensity shows a good match to experimental results for most investigated cases. In addition, the results are mostly insensitive to the variation of the mesh size.

Effect of installing branch-shaped fin on cold energy saving during freezing considering nanomaterial

This research examines the solidification through a finned tank containing alumina nano-powders and water as PCM (phase change material). Mathematical models were developed, assuming a uniform concentration of nano-powders and neglecting convective term effects. The model includes three time-dependent terms, discretized using an implicit approach, with solutions obtained via the Galerkin method and convergence achieved using an adaptive mesh. The thermal conductivity of NEPCM improves with increased concentration (ϕ), resulting in a faster transition from liquid NEPCM to ice. For pure water, the complete freezing time is 6795.38 s; however, with additives, this time is reduced by 26.78 %. Additionally, using powders with a higher "m" value further accelerates the freezing process, decreasing the completion time by about 6.98 %. The effect of powder configuration becomes more pronounced with increasing concentration. These findings are crucial for enhancing the sustainability of natural resources by improving cold storage and solidification processes.

A coupled fully implicit method for solving drag-adjoint equations of steady incompressible flows

Numerical instability is one of the main concerns when applying adjoint-based gradient computation in aerodynamic design optimization for a variety of engineering problems. An adjoint pressure-adjoint velocity-coupled fully implicit method for solving the adjoint equations of steady incompressible flows is developed in the present work, taking the aerodynamic drag as the optimization target. The finite volume method for cell-centered, collocated variables on unstructured grids is used for spatial discretization. A stabilization term based on pressure-weighted interpolation (PWI) of the adjoint velocity is added to the adjoint continuity equation to avoid spurious oscillations of adjoint pressure. All the terms of the continuous adjoint equations are discretized implicitly, including the adjoint transpose convection (ATC) term, which is regarded as one of the major sources of numerical instability. The resulting discretized equations are integrated into one linear system, and the adjoint fields can be obtained simultaneously. To prevent the diagonal element of the coefficient matrix of the linear system from getting too small, a singular value decomposition is applied to the diagonal block of the coefficient matrix, and a limiter is applied to the diagonal elements. The condition number of the coefficient matrix may be quite large, so a parallel sparse linear solver that effectively combines direct and iterative methods through a Schur complement approach is applied to solve the linear system. Compared to the staggered iterative solver, no damping or masking is needed for the ATC term in the proposed fully implicit method. There is no need to sacrifice numerical accuracy for numerical stability. This method has been tested in several benchmark cases, and the numerical results show good numerical stability and accuracy. The present method provides a sound basis for industrial applications of adjoint-based aerodynamic optimization methods.

On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations

In this paper, we are concerned about the lattice Boltzmann methods (LBMs) based on vector-kinetic models for hyperbolic partial differential equations. In addition to usual lattice Boltzmann equation (LBE) derived by explicit discretisation of vector-kinetic equation (VKE), we also consider LBE derived by semi-implicit discretisation of VKE and compare the relaxation factors of both. We study the properties such as H-inequality, total variation boundedness and positivity of both the LBEs, and infer that the LBE due to semi-implicit discretisation naturally satisfies all the properties while the LBE due to explicit discretisation requires more restrictive condition on relaxation factor compared to the usual condition obtained from Chapman-Enskog expansion. We also derive the macroscopic finite difference form of the LBEs, and utilise it to establish the consistency of LBEs with the hyperbolic system. Further, we extend this LBM framework to hyperbolic conservation laws with source terms, such that there is no spurious numerical convection due to imbalance between convection and source terms. We also present a D2Q9 model that allows upwinding even along diagonal directions in addition to the usual upwinding along coordinate directions. The different aspects of the results are validated numerically on standard benchmark problems.

URANOS-2.0: Improved performance, enhanced portability, and model extension towards exascale computing of high-speed engineering flows

We present URANOS-2.0, the second major release of our massively parallel, GPU-accelerated solver for compressible wall flow applications. This latest version represents a significant leap forward in our initial tool, which was launched in 2023 (De Vanna et al. [1]), and has been specifically optimized to take full advantage of the opportunities offered by the cutting-edge pre-exascale architectures available within the EuroHPC JU. In particular, URANOS-2.0 emphasizes portability and compatibility improvements with the two top-ranked supercomputing architectures in Europe: LUMI and Leonardo. These systems utilize different GPU architectures, AMD and NVIDIA, respectively, which necessitates extensive efforts to ensure seamless usability across their distinct structures. In pursuit of this objective, the current release adheres to the OpenACC standard. This choice not only facilitates efficient utilization of the full potential inherent in these extensive GPU-based architectures but also upholds the principles of vendor neutrality, a distinctive characteristic of URANOS solvers in the CFD solvers' panorama. However, the URANOS-2.0 version goes beyond the goals of improving usability and portability; it introduces performance enhancements and restructures the most demanding computational kernels. This translates into a 2× speedup over the same architecture. In addition to its enhanced single-GPU performance, the present solver release demonstrates very good scalability in multi-GPU environments. URANOS-2.0, in fact, achieves strong scaling efficiencies of over 80% across 64 compute nodes (256 GPUs) for both LUMI and Leonardo. Furthermore, its weak scaling efficiencies reach approximately 95% and 90% on LUMI and Leonardo, respectively, when up to 256 nodes (1024 GPUs) are considered. These significant performance advancements position URANOS-2.0 as a state-of-the-art supercomputing platform tailored for compressible wall turbulence applications, establishing the solver as an integrated tool for various aerospace and energy engineering applications, which can span from direct numerical simulations, wall-resolved large eddy simulations, up to most recent wall-modeled large eddy simulations. Program summaryProgram title: Unsteady Robust All-around Navier-StOkes Solver (URANOS)CPC Library link to program files:https://doi.org/10.17632/pw5hshn9k6.2Developer's repository link:https://github.com/uranos-gpu/uranos-gpu, https://github.com/uranos-gpu/uranos-gpu/tree/v2.0Licensing provisions: BSD License 2.0Programming language: Modern Fortran, OpenACC, MPINature of problem: Solving the compressible Navier-Stokes equations in a three-dimensional Cartesian framework.Solution method: Convective terms are treated with high-resolution shock-capturing schemes. The system dynamics is advanced in time with a three-stage Runge-Kutta method. Parallelization adopts MPI+OpenACC.

Elliptic problems with superlinear convection terms

In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type−div(M(x)∇u)=−div(h(u)E(x))+f(x), where M is a bounded elliptic matrix, the vector field E and the function f belong to suitable Lebesgue spaces, and the function s→h(s) features a superlinear growth at infinity. We provide some existence and non existence results for solutions to the associated Dirichlet problem and a comparison principle.

Numerical study of the drag force, interfacial area and mass transfer in bubbles in a vertical pipe

A systematic numerical study of drag force and mass transfer in gravity-driven bubbles in a vertical pipe is performed at Re∼O(100−1000). This research employs a parallel multi-marker unstructured conservative level set method for interface capturing, avoiding the numerical coalescence in bubble swarms. The finite volume method discretizes transport equations on 3D collocated unstructured meshes. Unstructured flux limiter schemes solve the convective term of transport equations, preserving the numerical stability at high Reynolds numbers and high-density ratios. Thermodynamic equilibrium is assumed at the interface for the concentration of chemical species. The hydrodynamics and mass transfer of bubbles are validated against classical correlations from the literature. Finally, direct simulations are executed to develop new correlations for the drag force, normalized bubble surface and Sherwood number for bubbles in a vertical pipe.

Development of an accurate central finite-difference scheme with a compact stencil for the simulation of unsteady incompressible flows on staggered orthogonal grids

In scale-resolving simulations such as Large Eddy Simulations (LES), the spatial discretization scheme of the convective term plays a crucial role in avoiding interference between the numerical errors and the subgrid-scale model. Accurate schemes lead to lower truncation errors and better predictions of turbulent flows without the need for an excessively refined grid. To this end, a new second-order finite-difference scheme (HCDS6) has been developed for incompressible flows and orthogonal staggered grids. Compared to the standard second-order scheme, the new scheme has significantly lower dispersion errors. Compared to existing high-order schemes, the numerical stencil of HCDS6 is more compact, which makes it easier to implement, especially considering boundary conditions around complex geometries using Immersed Boundary Methods (IBM). The HCDS6 scheme conserves the discrete momentum with limited production or dissipation of discrete kinetic energy, which guarantees its numerical stability. Its performance is evaluated using an open-source CFD package called REEF3D. Three benchmarks demonstrate the key properties and performance of the scheme: the convection of an isentropic vortex, the Taylor-Green vortex flow, and turbulent channel flow. Its relatively low dispersion errors, combined with ease of implementation, make the HCDS6 scheme a promising candidate for efficient scale-resolving simulations of turbulent flows.

Inf-sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids for Navier–Stokes equations

This paper considers the discretization of the time-dependent Navier–Stokes equations with the family of inf-sup stabilized Scott–Vogelius pairs recently introduced in [John/Li/Merdon/Rui, Math. Models Methods Appl. Sci., 2024] for the Stokes problem. Therein, the velocity space is obtained by enriching the H1-conforming Lagrange element space with some H(div)-conforming Raviart–Thomas functions, such that the divergence constraint is satisfied exactly. In these methods arbitrary shape-regular simplicial grids can be used.In the present paper two alternatives for discretizing the convective terms are considered. One variant leads to a scheme that still only involves volume integrals, and the other variant employs upwinding known from DG schemes. Both variants ensure the conservation of linear momentum and angular momentum in some suitable sense. In addition, a pressure-robust and convection-robust velocity error estimate is derived, i.e., the velocity error bound does not depend on the pressure and the constant in the error bound for the kinetic energy does not blow up for small viscosity. After condensation of the enrichment unknowns and all non-constant pressure unknowns, the method can be reduced to a Pk−P0-like system for arbitrary velocity polynomial degree k. Numerical studies verify the theoretical findings.

A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity

A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier–Stokes equations coupled to the convection–conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conductivity are temperature-dependent under the Boussinesq assumption. The proposed method consists of four steps all based on a viscosity-splitting algorithm where the convection and diffusion terms of both velocity and temperature solutions are separated while a viscosity term is kept in the correction step at all times. This procedure preserves the original boundary conditions on the corrected velocity and it removes any pressure inconsistencies. As a main feature, our method allows the temperature to be transported by a non-divergence-free velocity, in which case we show how to handle the subtle temperature convection term in the error analysis and establish full first-order error estimates for the velocity and the temperature solutions and 1/2-order estimates for the pressure solution in their appropriate norms. The theoretical results are examined by an accuracy test example with known analytical solution and using a benchmark problem of Rayleigh–Bénard convection with temperature-dependent viscosity and thermal conductivity. We also apply the method for solving a problem of unsteady flow over a heated airfoil. The obtained results demonstrate the convergence, accuracy and applicability of the proposed time viscosity-splitting method.

Macroscopic finite-difference scheme and modified equationsof the general propagation multiple-relaxation-time lattice Boltzmann model.

In this paper we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations(MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation(NACDE) and Navier-Stokes equations(NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation(CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, three benchmark problems, the Gauss hill problem, the CDE with nonlinear convection and diffusion terms, and the Taylor-Green vortex flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results not only are in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis.