Numerical Diffusion Research Articles

Compositional reservoir simulation with a high-resolution compact stencil adaptive implicit method

The adaptive implicit method (AIM) is the mainstream approach for compositional reservoir simulation. In its standard form, AIM uses single-point upwinding to reconstruct the fluxes across the interfaces of the control volume, and this leads to substantial numerical diffusion and loss of accuracy. Previous efforts to improve the accuracy of AIM focused on using high-order schemes to reconstruct the interfacial fluxes; those schemes introduced additional numerical nonlinearities to the system of equations or compromised the accuracy of the Jacobian by neglecting the high-order terms in its construction. In this work, we describe a high-resolution compact-stencil (HRCS) AIM. The new scheme is applied to compositional reservoir simulation. In addition to the mixed implicit/explicit time discretization of standard AIM, the HRCS AIM scheme uses a mixed time and space discretization. Specifically, we blend low- and high-order fluxes according to a well defined rule that uses a high-order reconstruction in the explicit regions of the domain and a low-order reconstruction in the implicit regions. This strategy ensures that additional nonlinearities introduced by the high-order reconstruction do not impact the Jacobian matrix, thus preserving the algebraic structure of standard AIM. The HRCS AIM method is demonstrated using several compositional problems. The results indicate substantial gains in accuracy with a small additional computational cost compared with standard AIM. Additionally, HRCS AIM is more robust and has a smaller computational cost compared with its full high-resolution counterpart.

Semi-Lagrangian simulation of particle laden flows using an SPH framework

Particle–laden flows occur in many natural and industrial systems and simulating them can be particularly challenging. The coupling of smoothed particle hydrodynamics (SPH) with the discrete element method (DEM) can effectively simulate particle-laden multiphase fluid dynamical systems, due to the shared Lagrangian nature of both methods. However, this approach has some inherent shortcomings, including a prohibitively small time step when dealing with small particles. An alternative approach is to use an Eulerian-Eulerian reference frame, usually using finite element or finite volume discretisations. In this approach, momentum and continuity equations are solved for each discrete phase as well as the continuous phase, and particles are modelled by means of concentration and velocity fields. This approach can suffer from strong numerical diffusion in the advection of the concentrations when absolute velocities of the phases are high, whilst their relative velocities are small. This numerical diffusion can obscure important aspects of the behaviour as it can smooth out details, especially in the particle concentration fields. In order to mitigate the shortcomings of these existing techniques, we present a new SPH-based semi-Lagrangian framework for solving the momentum and continuity equations for all phases in particle-laden flows. In this framework, the discrete and continuous phases move relative to a reference frame that moves at a momentum-averaged velocity. By focusing on velocities relative to the reference frame our method substantially reduces numerical diffusion compared to traditional Eulerian-Eulerian approaches, at a lower computational cost compared to Lagrangian-Lagrangian approaches. The simulation approach is validated by means of comparisons to both computational and experimental results for a number of relevant systems including particle-liquid separation in an inclined channel, particle sedimentation in a liquid, and gas-particle fluidised beds. This new method is shown to compare very favourably in terms of both the accuracy of the results and the computational cost required to achieve them.

Improving approximation accuracy in Godunov-type smoothed particle hydrodynamics methods

The study examines the origin of errors resulting from the approximation of the right hand sides of the Euler equations using the Godunov type contact method of smoothed particle hydrodynamics (CSPH). The analytical expression for the numerical shear viscosity in CSPH method is obtained. In our recent study the numerical viscosity was determined by comparing the numerical solution of momentum diffusion in the shear flow with theoretical one. In this study we deduce the analytical expression for the numerical viscosity which is found to be similar to numerical one, confirming the obtained results. To reduce numerical diffusion, diffusion limiters are typically applied to expressions for contact values of velocity and pressure, as well as higher-order reconstruction schemes. Based on the performed theoretical analysis, we propose a new method for correcting quantities at interparticle contacts in CSPH method, which can be easily extended to the MUSCL-type (Monotonic Upstream-centered Scheme for Conservation Laws) method. Original CSPH and MUSCL-SPH approaches and ones with aforementioned correction are compared.

Melt embayments record multi-stage magma decompression histories

Over the last decade, the melt embayment has proven its merit as a robust petrological tool capable of recording magma decompression rates for explosive eruptions. However, the models developed and applied to extract this information from embayments have not accounted for the complexity and nonlinearity of magma flow in the conduit. We present Embayment Decompression in Two Stages (EDiTS): a numerical model for extracting magma decompression rates from measured volatile diffusion profiles preserved in crystal-hosted embayments, approximating magma acceleration using two constant-rate decompression paths. This model solves for three unknown parameters: initial (deeper) and final (shallower) decompression rates, as well as the pressure where a transition occurs. We successfully benchmark EDiTS against existing numerical diffusion models, and use controlled multi-stage decompression experiments on natural quartz-hosted embayments to test the ability of our model to recover known decompression paths. We find that EDiTS is able to closely approximate the known two-stage path in the mixed-volatile (H2O + CO2) experiment, while a constant-rate modeling approach is unable to simultaneously fit H2O and CO2 gradients. However, in the H2O-saturated experiment, there is no unique solution to the resulting gradient, with both constant-rate and two-stage models reproducing the measured profile, and EDiTS notably overestimating the known total ascent time by several hours. Using decompression experiments, we show that constant-rate models can provide misleadingly good fits to embayment H2O gradients produced by more complex decompression histories, and thus the measurement and modeling of multiple diffusing species, when available, can provide crucial constraints. We then apply EDiTS to re-evaluate mixed-volatile embayment datasets from explosive silicic arc and caldera-forming eruptions from five volcanic centers (Yellowstone, WY, USA; Bandelier, NM, USA; Long Valley, CA, USA; Taupo, NZ; Mount St. Helens, WA, USA), where all systems contain initial CO2. In contrast to the minutes to hours of total ascent time extracted from embayment volatile profiles using constant-rate models, our two-stage model resolves slower initial ascent times that span several to >10 h. Final ascent rates are 1–2 orders of magnitude faster than the initial extracted rates, in agreement with theoretical conduit flow model predictions. Application of EDiTS to embayments from the May 18th, 1980 eruption of Mount St. Helens results in an initial stage of ascent on the order of hours consistent with the timing of magma arrival at the surface from the seismically-inferred storage region (7–9 km) ~3.5 h after the initial blast, and a final stage of ascent (<1–5 min) in close agreement with time-integrated bubble number densities. Our combined numerical, experimental, and natural results suggest that, with the application of more advanced models, the melt embayment can provide a complete picture of magma decompression timescales from the deep conduit to the surface.

Spurious numerical mixing under strong tidal forcing: a case study in the south-east Asian seas using the Symphonie model (v3.1.2)

Abstract. The role of mixing between layers of different densities is key to how the ocean works and interacts with other components of the Earth's system. Correctly accounting for its effect in numerical simulations is therefore of utmost importance. However, numerical models are still plagued with spurious sources of mixing, originating mostly from the vertical advection schemes in the case of fixed-coordinate models. As the number of phenomena explicitly resolved by models increases, so does the amplitude of resolved vertical motions and the amount of spurious numerical mixing, and regional models are no exception to this. This paper provides a clear illustration of this phenomenon in the context of simulating the south-east Asian (SEA) seas along with a simple way to reduce its impact. This region is known for its particularly strong internal tides and the fundamental role they play in the dynamic of the region. Using the Symphonie ocean model, simulations including and excluding tides and using a pseudo-third-order upwind advection scheme on the vertical are compared to several reference datasets, and the impact on water masses is assessed. The high diffusivity of this advection scheme is demonstrated along with the importance of accounting for tidal mixing for a correct representation of water masses. Simultaneously, we present an improvement in this advection scheme to make it more suitable for use in the vertical. Simulations with the new formulation are added for comparison. We conclude that the use of a higher-order numerical diffusion operator greatly improves the overall performance of the model.

A Fully Implicit Coupled Scheme for Mixed Elastohydrodynamic Problems on Co-Allocated Grids

In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate.

Nonequilibrium fast-lithiation of Li4Ti5O12 thin film anode for LIBs

Li4Ti5O12 (LTO) is known for its zero-strain characteristic in electrochemical applications, making it a suitable material for fast-charging applications. Here, we systematically studied the quasi-equilibrium and non-equilibrium lithium-ion transportation kinetics in LTO thin-film electrodes, across a range of scales from the crystal lattice to the microstructured electrodes. At the crystal lattice scale, during the non-equilibrium lithiation process, lithium ions are dispersedly embedded into the 16c position, resulting in more 8a → 16c migration compared with the quasi-equilibrium lithiation, and forming numerous fast lithium diffusion channels inside the LTO lattice. At the microstructural electrode scale, optical spectrum characterizations supported the “nano-filaments” lithiation model in polycrystalline LTO thin-film electrodes during the lithiation process. Our results reveal the patterns of lithium migration and distribution within the LTO thin film electrode under the non-equilibrium and quasi-equilibrium lithiation process, offering profound insights into the potential optimization strategies for enhancing the performance of fast-charging thin film batteries.

Massively parallel axisymmetric fluid model for streamer discharges

A highly parallelizable fluid plasma simulation tool based upon the first-order drift-diffusion equations is discussed. Atmospheric pressure plasmas have densities and gradients that require small element sizes in order to accurately simulate the plasm resulting in computational meshes on the order of millions to tens of millions of elements for realistic size plasma reactors. To enable simulations of this nature, parallel computing is required and must be optimized for the particular problem. Here, a finite-volume, electrostatic drift-diffusion implementation for low-temperature plasma is discussed. The implementation is built upon the Message Passing Interface (MPI) library in C++ using Object Oriented Programming. The underlying numerical method is outlined in detail and benchmarked against simple streamer formation from other streamer codes. Electron densities, electric field, and propagation speeds are compared with the reference case and show good agreement. Convergence studies are also performed showing a minimal space step of approximately 4 μm required to reduce relative error to below 1% during early streamer simulation times and even finer space steps are required for longer times. Additionally, strong and weak scaling of the implementation are studied and demonstrate the excellent performance behavior of the implementation up to 100 million elements on 1024 processors. Finally, different advection schemes are compared for the simple streamer problem to analyze the influence of numerical diffusion on the resulting quantities of interest.

Numerical modeling and validation of dike-induced water flow dynamics using OpenFOAM

ABSTRACT The basic purpose of the present research is to numerically elucidate the flow around a single dike in four different geometric configurations (CN: no cylinders, C5: 5 cylinders, C10: 10 cylinders, C15: 15 cylinders), under conditions of a constant flow rate and subcritical flow. This involved substituting the impermeable dike with varying numbers of piles to validate the observed experimental flow patterns, particularly the conditions leading to reverse flow formation. OpenFOAM, an open-source algorithm, was utilized for the simulation, incorporating the volume of fluid (VOF) method. Accurately depicting the reverse flow formation with minimal numerical diffusion, a strategy involving multizone meshing and the application of mesh refinement zones was utilized. These refinements were particularly focused on the section between 1.8 m and 2.2 m within the numerical domain. The water surface profile in front section of the dike and the averaged velocity at five different locations, which were then compared with the numerical results. The numerically predicted streamwise velocity showed a percentage error ranging between 0.5% and 4.5%. The numerical results from this study are pivotal in dike design, aiming to mitigate accelerated wear during flood events and to protect both the dike head and the adjacent bank from high energy flow failures.

Conservative transport model for surfactant on the interface based on the phase-field method

We propose a new surfactant transport model on the interface based on the phase-field method. The new model has two features: (a) preventing surfactants on the interface from leaking out of the interface due to numerical diffusion even when the diffusion coefficient is extremely low, and (b) satisfying the conservation of surfactant mass. The concentration profile on the interface is matched to the surface delta function to prevent numerical diffusion, and the finite volume method is applied to the resulting model to satisfy the conservation of surfactant mass. The proposed model is incorporated in a weakly compressible scheme and applied in several numerical tests related to incompressible two-phase flows with surfactants. Numerical results show that the proposed model can be applied to various incompressible two-phase flow simulations with surfactant.

Best-estimate water hammer simulations to avoid the calculation of unrealistically high loads or unphysical pressure and force peaks

For safety-related systems fluid loads due to fluid transients have to be quantified for subsequent structural analyses to ensure their integrity or function, as required. Usually transient fluid loads in pipe systems are determined with one-dimensional water hammer software. For single-phase liquid flow, the method of characteristics (MOC) is often used that gives in this case appropriate results. For the consideration of local vapor bubbles, the MOC is combined with the discrete vapor cavity model (DVC). The DVC model may generate unrealistic pressure spikes due to the calculation of the collapse of multi-cavities in scenarios, where only one vapor bubble should actually occur. The application of a two-phase code may improve the calculation results. One requirement for the latter codes is the ability to calculate the propagation of steep gradients without suffering from numerical diffusion to exclude the underestimation of fluid loads. This is commonly attained by applying higher-order numerical schemes. However, the application of a numerical method of pure 2nd order leads to the calculation of unphysical oscillations at steep gradients causing severe problems during the solution. To exclude this, numerical methods with flux limiters can be used. With their application, the calculation of unrealistically high loads due to numerical deficiencies can be minimized. In addition, the consideration of further physical effects, that lead to the reduction of loads during transient flow processes, allows for a more realistic calculation of the loads. These are unsteady friction, widening of the pipe caused by pressure increase, fluid-structure interaction at junctions and due to friction, degassing of gas that is initially dissolved physically in a liquid and thermodynamic non-equilibrium during vapor bubble collapse. The in-house code DYVRO applies a second-order accurate scheme with flux limiters based on the Godunov method and can account for the above-described physical phenomena. It is shown by comparison of calculation results obtained by DYVRO with experimental data from literature that with modeling of these physical effects the loads can be calculated more realistically. Generally, these loads are lower than the results calculated by simplified models, which do not account for these effects. Considering that these loads are applied in subsequent structural analyses, cost-intensive oversizing of pipes and their supports can be avoided, by ensuring the necessary safety.

Controlling numerical diffusion in solving advection-dominated transport problems

Numerical schemes for advection-dominated transport problems are are evaluated in a comparative study. Explicit and implicit finite difference methods are analyzed together with a global random walk algorithm in the frame of a splitting procedure. The efficiency of the methods with respect to the control of the numerical diffusion is investigated numerically on one-dimensional problems with constant coefficients and two-dimensional problems with variable coefficients consisting of realizations of space-random functions.

A Novel Connection Element Method for Multiscale Numerical Simulation of Two-Phase Flow in Fractured Reservoirs

Summary This paper presents a novel approach to the numerical simulation of fractured reservoirs, called the connection element method (CEM), which differs from traditional grid-based methods. The reservoir computational domain is discretized into a series of nodes, and a system of connection elements is constructed based on the given connection lengths and angles. The pressure diffusion term is approximated using generalized finite difference theory. Meanwhile, the transmissibility and volume of the connection elements are determined, and pressure equations are solved discretely to obtain pressure at nodes to approximate the upstream flux along connection elements. Then, we solve the transport equation to obtain oil saturation profiles with low numerical diffusion, utilizing the discontinuous Galerkin (DG) method. Moreover, the flow path tracking algorithm is introduced to quantify the flow allocation factors between wells. In all, the pressure equation can be solved at a global coarse-scale point cloud and the saturation equation is calculated at a local fine-scale connection element. In other words, CEM is of multiscale characteristics relatively. Finally, several numerical examples are implemented to demonstrate that CEM can achieve a relatively better balance between computational accuracy and efficiency compared with embedded discrete fracture modeling (EDFM). Furthermore, CEM adopts flexible meshless nodes instead of grids with strong topology, making it more practical to handle complex reservoir geometry such as fractured reservoirs.

A block-spectral adaptive H-/p-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y1Δy1+∂V/∂y2Δy2+∂W/∂y3Δy3 is calculated and normalized by the local speed of sound, a. The grid spacing, Δxi, is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p=0 to p=pmax in regions of weak compression, (ΔU/a)crit<ΔU/a<0 and kept at p=pmax in regions of flow expansion ΔU/a≥0, while staying at the H=0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a<(ΔU/a)crit, are H-refined up to H=Hmax where Hmax is applied at the location of maximum compression, ΔU/a=min(ΔU/a) in the domain, while keeping p=0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a)crit= -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p=0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

Eulerian–Lagrangian hybrid solvers in external aerodynamics: Modeling and analysis of airfoil stall

Hybrid computational solvers that integrate Eulerian and Lagrangian methods are emerging as powerful tools in computational fluid dynamics, particularly for external aerodynamics. These solvers rely on the strengths of both approaches: Eulerian methods efficiently handle boundary layers, while Lagrangian methods excel in reducing numerical diffusion in flow convection. Building on our prior development of a two-dimensional hybrid solver that combines OpenFOAM with vortex particle method, this paper extends its application to the complex phenomena of airfoil stall at low Reynolds numbers. Specifically, we examine both static and dynamic stall conditions of a National Advisory Committee for Aeronautics (NACA) airfoil series 0012 (NACA0012) across a wide range of attack angles and oscillation frequencies, comparing our results with established data. The findings demonstrate the accuracy of hybrid Eulerian–Lagrangian solvers in replicating known stall behaviors, underscoring their potential for advanced aerodynamic studies. This work not only confirms the capability of hybrid solvers in accurately modeling challenging flows but also paves the way for their increased involvement in the field of external aerodynamics.

An Approach for Modeling the Orographic–Forcing Effect via Random Cascades and the Long‐Term Statistics of Mexico City's Daily Precipitation

AbstractThe orographic effect on the spatial structure of precipitation is a fundamental problem in hydrometeorology that still requires a better understanding of the physical processes involved in the emergence of rainfall patterns and their complex statistical structure. In tropical regions, where meteorological measurements are notoriously sparse and data quality control is often poor or missing, the study of precipitation modeling and prediction is challenging. This research aims to show an innovative approach based on a random cascade downscaling method to generate high‐resolution precipitation products from coarse‐scale precipitation products. This approach also includes a topographic enhancement function for describing the altitudinal variability of precipitation and a numerical diffusion filter to lessen the blockiness problem of random cascades. The suggested approach was applied to analyze some long‐term precipitation statistics in the metropolitan area of Mexico City. The model result agrees closely with the temporal statistics of the selected precipitation products and reflects complex orographic constraints. The proposed downscaling approach becomes an alternative to expensive computational methods and allows urban hydrology applications and analysis of small watersheds to incorporate the effects of complex orography.

A Block Triple-Relaxation-Time Lattice Boltzmann Method for Solid–Liquid Phase Change Problem

This study introduces a block triple-relaxation-time (B-TriRT) lattice Boltzmann model designed specifically for simulating melting phenomena within a rectangular cavity subject to intense heating from below, characterized by high Rayleigh (Ra) numbers (Ra=108). Through benchmark testing, it is demonstrated that the proposed B-TriRT approach markedly mitigates numerical diffusion along the phase interface. Furthermore, an examination of the heated region’s placement is conducted, revealing its significant impact on the rate of melting. Notably, findings suggest that optimal melting occurs most rapidly when the heated region is positioned centrally within the cavity.

MATRICS: The implicit matrix-free Eulerian hydrodynamics solver

Context. There exists a zoo of different astrophysical fluid dynamics solvers, most of which are based on an explicit formulation and hence stability-limited to small time steps dictated by the Courant number expressing the local speed of sound. With this limitation, the modeling of low-Mach-number flows requires small time steps that introduce significant numerical diffusion, and a large amount of computational resources are needed. On the other hand, implicit methods are often developed to exclusively model the fully incompressible or 1D case since they require the construction and solution of one or more large (non)linear systems per time step, for which direct matrix inversion procedures become unacceptably slow in two or more dimensions. Aims. In this work, we present a globally implicit 3D axisymmetric Eulerian solver for the compressible Navier–Stokes equations including the energy equation using conservative formulation and a fully simultaneous approach. We use the second-order-in-time backward differentiation formula for temporal discretization as well as the κ scheme for spatial discretization. We implement different limiter functions to prohibit the occurrence of spurious oscillations in the vicinity of discontinuities. Our method resembles the well-known monotone upwind scheme for conservation laws (MUSCL). We briefly present efficient solution methods for the arising sparse and nonlinear system of equations. Methods. To deal with the nonlinearity of the Navier–Stokes equations we used a Newton iteration procedure in which the required Jacobian matrix-vector product was reconstructed with a first-order finite difference approximation to machine precision in a matrix-free way. The resulting linear system was solved either completely matrix-free with a combination of a sufficient Krylov solver and an approximate Jacobian preconditioner or semi-matrix-free with the incomplete lower upper factorization technique as a preconditioner. The latter was dependent on a standalone approximation of the Jacobian matrix, which was optionally calculated and needed solely for the purpose of preconditioning. Results. We show our method to be capable of damping sound waves and resolving shocks even at Courant numbers larger than one. Furthermore, we prove the method’s ability to solve boundary value problems like the cylindrical Taylor-Couette flow (TC), including viscosity, and to model transition flows. To show the latter, we recover predicted growth rates for the vertical shear instability, while choosing a time step orders of magnitude larger than the explicit one. Finally, we verify that our method is second order in space by simulating a simplistic, stationary solar wind.

Flow around a pair of 2D cylinders using a hybrid Eulerian-Lagrangian solver

The field of external aerodynamics encompasses various engineering disciplines with a significant impact on wind energy technology. Aerodynamic investigations provide insights not only into the characteristics of individual blades or standalone wind turbines but also into entire wind farms. As advancements in wind turbine design continue, understanding the interactions between turbines in close proximity becomes crucial, presenting a multi-body problem. Researchers require efficient and accurate tools to comprehensively study such dynamics. This paper presents a hybrid Eulerian-Lagrangian solver designed to leverage the strengths of Eulerian solvers in resolving boundary layers and Lagrangian solvers in convecting wakes downstream without introducing significant numerical diffusion. The solver adeptly handles multi-body simulations, allowing the construction of independent Eulerian meshes that communicate seamlessly through Lagrangian particles. In this way, the computational study of multibody problems does not require very large and dense meshes. Validation in single-body cases has already been conducted, with this paper demonstrating the solver’s application to a pair of cylinders in different configurations. A comparative performance analysis is carried out against pure Eulerian solvers. The results highlight that the hybrid solver efficiently reproduces the accuracy of the Eulerian solver, demonstrating its effectiveness in handling complex aerodynamic simulations.

Optimized compact finite volume formulation with dispersion relation preserving characteristics in structured space discretizations

Computationally extensive fluid flow simulations usually require numerical schemes with a high degree of numerical precision, where high wavenumber and frequency capturing capability is desired in solutions with high physical fidelity. Numerical dispersion and diffusion errors must be reduced to a minimum in order to caputre low amplitude and high frequency flow aspects, such as flow induced sound waves and minor instabilities. Such schemes also must be capable of dealing with flow discontinuities, such as shockwaves and expansion waves in cases where the flow velocity stands near or above sound velocity. In this work the Dispersion Relation Preserving (DRP) optimization is formally extended to the compact Finite Volume (FV) framework where the error is minimized along a given spectral interval. This is done by equaling the resulting algebraic compact spectral optimized Finite Difference (FD) operators with the Finite Volume formulation with the desired numeric characteristics. Numerical tests are carried over linear and nonlinear governing equations models for one and three-dimensional cases, where the travelling Gaussian wave, the transient expansion wave and the smooth to nonsmooth step wave flows are considered. The proposed compact DRP FV schemes surpasses its counterparts in some numerical tests while maintaining comparable capabilities with other more basic schemes in the remaining numerical tests. Excellent broadband content capturing capability is observed, while possessing reduced numerical instabilities generation.