Effect Of Numerical Diffusion Research Articles

Gas composition tracking feasibility using transient finite difference [formula omitted]-scheme model for binary gas mixtures

Implicit finite difference method is popular numerical method for simulation of transient pipeline dynamics, governed by the system of Euler partial differential equations. If advection equation is included in the mathematical formulation, gas composition tracking is also possible. If implicit scheme is used for gas composition tracking, simulated concentration profiles are distorted due to the occurrence of numerical diffusion, a non-physical phenomenon, caused by the 1st order accurate numerical implicit scheme. Intensity of the numerical diffusion can be decreased by use of θ-scheme with arbitrarily chosen implicitness. In order to evaluate accuracy of such numerical scheme and adequacy for usage in actual application, numerical model must be evaluated on actual gas pipeline system topology with actual measured boundary conditions and compared to actual measured results. Aim of this paper is to assess whether hydrogen concentration tracking is feasible using such approach considering complex grid topologies. Paper highlights the peculiarities of the proposed θ-scheme and finite difference method and its impact on the calculated concentration profile for binary gas mixtures. Non-physical flow reversal issue and its impacts on concentration tracking in looped pipeline system is researched and explained. Simulation results shows high accuracy for simulated values of hydraulic variables compared to the measured values, in some cases fit is perfect. Discrepancy between measured and the simulated values of the pressures at nodes on the main transport route is negligible, while the discrepancy increases with the distance from the main transport routes. The largest discrepancy occurred on the most distant node and was between 1.7006 bar (4.85%) and 1.7119 bar (4.88%), depending on the θ value. On the other hand, simulated concentration profile lacks finer details due to the numerical diffusion effects while the simulated concentration profile lags the measured profile, partly by the impacts of the 1st order accurate scheme and partly by effects of non-physical reversed flows. Discrepancy between simulated and measured amplitude of the tracked concentration profile was negligible, while discrepancy due to the time delay of the simulated and measured profile was more expressed and ranged between 2h to 9h. Largest time delay was caused by the non-physical flow reversal.

In uence of numerical diffusion on the growth rate of viscous ngers in the numerical implementation of the Peaceman model by the finite volume method

A numerical model of oil displacement by a mixture of water and polymer based on the Peaceman model is considered. Numerical experiments were carried out using the DuMux package, which is a software library designed for modeling nonstationary hydrodynamic problems in porous media. The software package uses the vertex-centered variant of finite volume method. The effect of diffusion on the growth rate of ''viscous fingers'' has been studied. The dependencies of the leading front velocity on the value of model diffusion are obtained for three viscosity models. It is shown that the effect of numerical diffusion on the growth rate of ''viscous fingers'' imposes limitations on calculations for small values of model diffusion.

Modelling interactions between waves and diffused interfaces

AbstractWhen simulating multiphase compressible flows using the diffuse‐interface methods, the test cases presented in the literature to validate the modellings with regard to interface problems are always textbook cases: interfaces are sharp and the simulations therefore easily converge to the exact solutions. In real problems, it is rather different because the waves encounter moving interfaces which consequently have already undergone the effects of numerical diffusion. Numerical solutions resulting from the interactions of waves with diffused interfaces have never been precisely investigated and for good reasons, the results obtained are extremely dependent on the model used. Precisely, well‐posed models present similar and important issues when such an interaction occurs, coming from the appearance of a wave‐trapping phenomenon. To circumvent those issues, we propose to use a thermodynamically‐consistent pressure‐disequilibrium model with finite, instead of infinite, pressure‐relaxation rate to overcome the difficulties inherent in the computation of these interactions. Because the original method to solve this model only enables infinite relaxation, we propose a new numerical method allowing infinite as well as finite relaxation rates. Solutions of the new modeling are examined and compared to literature, in particular we propose the study of a shock on a water–air interface, but also for problems of helium–air and water–air shock tubes, spherical and nonspherical bubble collapses.

Aerodynamic Analysis of a Supersonic Transport Aircraft at Low and High Speed Flow Conditions

The recent improvement of technology readiness level in aeronautics and the renewed demand for faster transportation are driving the rebirth of supersonic flight for commercial aviation. However, the design of a future supersonic aircraft is still very challenging due to the complexity of several problems, such as static stability performance during the acceleration phase from subsonic speeds to supersonic speeds. Additionally, the interest of scientific community in open source numerical platform as a valid tool for a reliable and affordable aerodynamic design is considerably growing. In this framework, the present work addresses the aerodynamic performance of a Concorde-like aeroshape developed within the preliminary design of a high-speed civil transportation aircraft. Several flight conditions, ranging from subsonic to supersonic speeds, were investigated in detail by using Computational Fluid Dynamics. The aerodynamic force and moment coefficients are computed with fully three-dimensional and steady state Reynolds Average Navier-Stokes simulations, carried out in turbulent flow conditions. The effect of the Mach number variation on the shift of the aircraft aerodynamic center is detailed, by focusing on the aircraft pitching static stability. Flowfield numerical simulations are performed with both commercial (Ansys-Fluent) tool and open-source (SU2) code, which is also used extensively in multidisciplinary design procedures, for further comparisons. Particular attention is focused on the shift of the aeroshape aerodynamic center to verify that the provided wing design allows the aircraft static margin to be within 5% of the reference length, both at low-speed and high-speed flight conditions. The computed positions of the aerodynamic center are in agreement with the aeroshape surface pressure distributions and confirmed the literature results available for the Concorde aircraft. Therefore, in the view of future simulation campaigns for supersonic transportation aircraft, the present work aims to bridge the gap between previous aerodynamic design experiences, for instance matured on Concorde, and those carried out with modern CFD tools on full-scale aircraft, and on time-scales compatible with conceptual design practice. Finally, as the difference between the computed aerodynamic coefficients reflected mainly on drag computation performed with SU2, a special focus on numerical diffusion effect of the solver is also given and compared with a commercial certified CFD tool. This adds a unique further contribution to the SU2 community for aeronautics application.

A resolution criterion based on characteristic time-scales for MHD simulations of molecular clouds

ABSTRACT We investigate the effect of numerical magnetic diffusion in magnetohydrodynamic (MHD) simulations of magnetically supported molecular clouds. To this end, we have performed numerical studies on adaptive mesh isothermal simulations of marginally subcritical molecular clouds. We find that simulations with low and intermediate resolutions collapse, contrary to what is theoretically expected. However, the simulation with the highest numerical resolution oscillates around an equilibrium state without collapsing. In order to quantify the numerical diffusion of the magnetic field, we ran a second suit of current-sheet simulations in which the numerical magnetic diffusion coefficient can be directly measured and computed the corresponding diffusion times at various numerical resolutions. On this basis, we propose a criterion for the resolution of magnetic fields in MHD simulations based on requiring that the diffusion time to be larger than the characteristic time-scale of the physical process responsible for the dynamic evolution of the structure.

Numerical Considerations in the Simulation of Equatorial Spread F

AbstractThe ionospheric irregularities known as equatorial spread F (ESF) have drawn great attention in decades due to their disruption of communications and navigation systems. ESF is generally attributed to Rayleigh–Taylor instability, but there are still many remaining issues about its formation and evolution. Numerical simulations have been widely used to study such a phenomenon due to the complex nonlinear evolution of ESF. A two‐dimensional ESF model was developed in this work and a series of experiments were conducted to study the effects of grid resolution and numerical diffusion on idealized ESF simulation. It was found that advection schemes with the total variation diminishing property are preferred for preventing spurious oscillations which occur near the steep density gradients in the ESF. On the other hand, schemes with low diffusion are also desirable in order to model complicated dynamic structures of the ESF. Moreover, numerical experiments suggest that some of the secondary instabilities in idealized ESF simulations, although with morphological similarities, are possibly initiated by numerical seeding, which may differ from the observed evolution of secondary ESF.

The Numerical Diffusion Effect on the CFD Simulation Accuracy of Velocity and Temperature Field for the Application of Sustainable Architecture Methodology

Numerical simulation of fluid flow and heat or mass transfer phenomenon requires numerical solution of Navier–Stokes and energy-conservation equations, together with the continuity equation. The basic problem of solving general transport equations by the Finite Volume Method (FVM) is the exact calculation of the transport quantity. Numerical or false diffusion is a phenomenon of inserting errors in calculations that threaten the accuracy of the computational solution. The paper compares the physical accuracy of the calculation in the Computational Fluid Dynamics (CFD) code in Ansys Fluent using the offered discretization calculation schemes, methods of solving the gradients of the transport quantity on the cell walls, and the influence of the mesh type. The paper offers possibilities on how to reduce numerical errors. In the calculation area, the sharp boundary of two areas with different temperatures is created in the flow direction. The three-dimensional (3D) stationary flow of the fictitious gas is simulated using FVM so that only advective transfer, in terms of momentum and heat, arises. The subject of the study is to determine the level of numerical diffusion (temperature field scattering) and to evaluate the values of the transport quantity (temperature), which are outside the range of specified boundary conditions at variously set calculation parameters.

Computational Evaluation of Mixing Performance in 3-D Swirl-Generating Passive Micromixers

Computational Fluid Dynamics (CFD) tools are used to investigate fluid flow and scalar mixing in micromixers where low molecular diffusivities yield advection dominant transport. In these applications, achieving a numerical solution is challenging. Numerical procedures used to overcome these difficulties may cause misevaluation of the mixing process. Evaluation of the mixing performance of these devices without appropriate analysis of the contribution of numerical diffusion yields over estimation of mixing performance. In this study, two- and four-inlet swirl-generating micromixers are examined for different mesh density, flow and molecular diffusivity scenarios. It is shown that mesh densities need to be high enough to reveal numerical diffusion errors in scalar transport simulations. Two-inlet micromixer design was found to produce higher numerical diffusion. In both micromixer configurations, when cell Peclet numbers were around 50 and 100 for Reynolds numbers 240 and 120, the numerical diffusion effects were tolerable. However, when large cell Peclet number scenarios were tested, it was found that the molecular diffusivity of the fluid is completely masked by false diffusion errors.

Numerical analysis of spatial discretization schemes in ARES transport code for shielding calculation

The discrete ordinates method (SN) is one of the mainstream methods for radiation shielding calculation of nuclear systems. The accuracy of spatial discretization in the SN equations has a significant effect on the accuracy of the shielding calculations. This work numerically examines the error behavior of various spatial discretization schemes implemented in the ARES transport code for shielding calculations. The numerical diffusion effect, encountered when the uncollided flux component is significant, such as in fast neutron groups or multi-dimensional void regions, is studied by investigating the ray propagation problem and glancing void problem. Positivity is investigated in optically thick cells and multi-dimensional void regions using spatial discretization schemes that cannot preserve non-negativity. In addition, the local accuracy is examined through a series of one-cell problems with various exact flux smoothness conditions in the cell. The results indicate that local accuracy depends not only on the spatial discretization but also the smoothness of the exact flux. Globally, severe unphysical flux representations arise in the diamond difference (DD) scheme. Other zero-order schemes inhibit oscillation but present significant numerical diffusion, whereas finite element methods damp the oscillation quickly near the flux discontinuity and present better resilience against negativity than DD. All these results can provide guidelines on selection of spatial discretization in realistic applications.

Sensitivity Analysis and Numerical Diffusion Effects for Hyperbolic PDE Systems with Discontinuous Solutions. The Case of Barotropic Euler Equations in Lagrangian Coordinates

Sensitivity analysis (SA) is the study of how the output of a mathematical model is affected by changes in the inputs. SA is widely studied, due to its many applications: uncertainty quantifi-cation, quick evaluation of close solutions, and optimization, to name but a few. In this work we show that the classic SA techniques, in particular the continuous sensitivity equation (CSE) method, cannot be used if the mathematical model is a system of hyperbolic partial differential equations (PDEs) with discontinuous solutions. The problem arises from the fact that the CSE method requires the differentiation of the state variable: if the latter is discontinuous, this in turns generates Dirac delta functions in the sensitivity. The focus of the first part of this work is to define a system of sensitivity equations valid also in case of discontinuous state: in order to do that, we add a correction term based on the Rankine-Hugoniot conditions. In the second part of this work we illustrate with some numerical tests how some classical finite volume schemes (an exact Godunov method and a Roe-type method) do not converge to the analytical solution for the sensitivity, due to the numerical diffusion: for this reason, we present an anti-diffusive numerical scheme, which provides the correct results for the sensitivity. In this work we carry out the computation in detail for the barotropic Euler equations in Lagrangian coordinates, but the approach is general and can be applied to any hyperbolic system with discontinuous solutions.

Numerical investigation of turbulent swirling flows through an abrupt expansion tube

A numerical investigation of turbulent swirling flows through an abrupt expansion tube is reported. The TEFESS code, based on a staggered Finite Volume approach with the standard k-ε model and first-order numerical schemes built-in, was used to carry out all the computations. The code has been modified in the present work to incorporate the ASM and two second-order numerical schemes. The ASM, which includes the non-gradient convection terms arising from the transformation from Cartesian to cylindrical coordinates, was investigated for isothermal flows by applying it to the flow through an abrupt expansion tube with or without swirl flows. In addition, to investigate the effects of numerical diffusion on the predicted results, two second-order differencing schemes, namely, second-order upwind and the quadratic upstream interpolation, were used to compare with the first-order hybrid scheme. An abrupt expansion tube with non-swirling flow, predicted results using both the k-ε model and the ASM were in good agreement with measurements. For swirling flows, the calculated results suggested that the use of the ASM with a second-order numerical scheme leads to better agreement between the numerical results and experimental data, while the k-ε model is incapable of capturing the stabilizing effect of the swirl.

Fully implicit higher-order schemes applied to polymer flooding

In water-based EOR methods, active chemical or biological substances are added to modify the physical properties of the fluids or/and the porous media at the interface between oil and water. The resulting displacement processes are governed by complex interplays between the transport of chemical substances, which is largely linear and highly affected by numerical diffusion, and how these substances affect the flow by changing the properties of the fluids and the surrounding rock. These effects are highly nonlinear and highly sensitive to threshold parameters that determine sharp transitions between regions of very different behavior. Unresolved simulation can therefore lead to misleading predictions of injectivity and recovery profiles. Use of higher-order spatial discretization schemes have been proposed by many authors as a means to reduce numerical diffusion and grid-orientation effects. Most higher-order simulators reported in the literature are based on explicit time stepping, and only a few are implicit. One reason that fully implicit formulations are not widely used might be that it becomes quite involved to compute the necessary linearizations for modern high-resolution discretizations of TVD and WENO type. Herein, we solve this problem by using automatic differentiation. We also demonstrate that using lagged evaluation of slope limiters and WENO weights alleviates the nonlinearity of the discrete systems and improves the computational efficiency, without having an adverse effect on the stability and accuracy of the higher-resolution schemes. As an example of EOR, we consider polymer flooding, which involves complex and adverse phenomena like adsorption in the rock, degradation and in-situ chemical reactions, shear thinning/thickening, dead pore space, etc. Using a few idealized test cases, we compare and contrast explicit and fully implicit time stepping for a variety of high and low-resolution spatial discretizations.

Analytical Stability Analogue for a Single-Phase Natural-Circulation Loop

Numerical solutions for transient fluid flow in nuclear systems often suffer from the effects of numerical diffusion and damping making the assessment of system stability rather difficult. Efforts for coping with this problem include research and development of algorithms with improved fidelity for stability calculations as they apply to particular problems. Benchmarking exercises in comparison with specially designed experiments are necessary to verify algorithmic fidelity and guide the development and adjustments of the algorithms. In this paper, an analytical approach is introduced where a simple model—an analogue—is constructed such that the basic instability mechanisms are represented in a form that lends itself to analytical solutions that are free from the diffusion and damping problems that plague finite volume algorithms. Direct conclusions can be made regarding the stability of a system in the case where the analogue closely resembles the system under study. However, when the system is too complex for direct assessment, the stability fidelity of numerical solutions can be assessed by comparing the numerical solution for the simple system with the analytical solution and using the comparison to quantify any damping effects and justify the application of the numerical method to the complex representation of the real system under study. The theoretical analysis is supported by reference to recent test data in the NuScale Integral System Test (NIST) facility representing a scaled-down NuScale module.

No double detonations but core carbon ignitions in high-resolution, grid-based simulations of binary white dwarf mergers

We study the violent phase of the merger of massive binary white dwarf systems. Our aim is to characterize the conditions for explosive burning to occur, and identify a possible explosion mechanism of Type Ia supernovae. The primary components of our model systems are carbon-oxygen (C/O) white dwarfs, while the secondaries are made either of C/O or of pure helium. We account for tidal effects in the initial conditions in a self-consistent way, and consider initially well-separated systems with slow inspiral rates. We study the merger evolution using an adaptive mesh refinement, reactive, Eulerian code in three dimensions, assuming symmetry across the orbital plane. We use a co-rotating reference frame to minimize the effects of numerical diffusion, and solve for self-gravity using a multi-grid approach. We find a novel detonation mechanism in C/O mergers with massive primaries. Here the detonation occurs in the primary's core and relies on the combined action of tidal heating, accretion heating, and self-heating due to nuclear burning. The exploding structure is compositionally stratified, with a reverse shock formed at the surface of the dense ejecta. The existence of such a shock has not been reported elsewhere. The explosion energy ($1.6\times 10^{51}$ erg) and $^{56}$Ni mass (0.86 M$_\odot$) are consistent with a SN Ia at the bright end of the luminosity distribution, with an approximated decline rate of $\Delta m_{15}(B)\approx 0.99$. Our study does not support double-detonation scenarios in the case of a system with a 0.6 M$_\odot$ helium secondary and a 0.9 M$_\odot$ primary. Although the accreted helium detonates, it fails to ignite carbon at the base of the boundary layer or in the primary's core.

Effects of Numerical Diffusion on the Computation of Viscous Supersonic Flow Over a Flat Plate

The effects of numerical diffusion on the computation of supersonic viscous flow over a flat plate at zero incidences are numerically investigated. The inviscid flux terms in the Navier–Stokes equations are computed using three schemes, namely, van Leer’s Flux Vector Splitting, Liou and Steffen’s Advection Upstream Splitting Method (AUSM) and Jaisankar and Raghurama Rao’s Diffusion Regulated Local Lax Friedrichs (DRLLF) schemes. The results are correlated with the inherent numerical diffusion of these schemes. The study is also motivated by the necessity to examine whether reduced artificial viscosity can be used with the DRLLF scheme in computing viscous flows than was suggested in the original paper on inviscid computation. It is demonstrated that reduced artificial viscosity is not only possible, but it results in a scheme that is very efficient in the computation of the standard supersonic viscous flow over a flat plate, in that it is comparable in accuracy to the AUSM scheme in the boundary layer and better than it in shock resolution. Even with the reduced artificial viscosity suggested in this paper the DRLLF scheme shows good convergence behaviour comparable with the other two schemes.

Effect of numerical diffusion on the water mass transformation in eddy-resolving models

This study investigates the effect of numerical diffusion associated with advection schemes on water mass transformation in an eddy-resolving model. The effect of numerical diffusion is evaluated as a residual between the total water mass transformation and the explicit water mass transformation: the former is calculated as the sum of meridional streamfunction and the temporal change rate of an isopycnal surface depth, and the latter is directly calculated with the use of the tendency equation of density. This method is used for investigating a dependency of numerical diffusion on explicit diffusivity. It is found that idealized channel experiments are categorized into three regimes according to a magnitude of explicit diffusivity: numerical diffusion, transitional, and explicit diffusion regimes. The numerical diffusion regime is defined as the regime where explicit diffusion changes do not significantly impact the solution. The magnitude of numerical diffusion is independent of the explicit diffusivity there. In the transitional regime, explicit (numerical) diffusion works more (less) with higher explicit diffusivity. Explicit and numerical diffusions are comparably important there. The explicit diffusion becomes significantly large and the numerical diffusion is almost negligible in the explicit diffusion regime. The total diffusion effect on water mass transformation there is considerably larger than those in the two other regimes.Two experiments are conducted with a Southern Ocean model under a realistic configuration. These belong to the numerical diffusion and transitional regimes. The model becomes a little too diffusive in the latter experiment. This result and results of channel experiments indicate that it is not an adequate option for a realistic Southern Ocean simulation that we adopt a diffusion coefficient in the explicit diffusion regime in order to reduce levels of numerical diffusion. It indicates that numerical diffusion is inevitable for eddy-resolving models with horizontal resolution around 0.1° and we must adequately evaluate its effect on model results when analyzing outputs of such high resolution models. The method proposed in the current study for assessing numerical diffusion will be useful for investigating an eddying ocean with numerical models.

An adaptive-grid model for dynamic simulation of thermocline thermal energy storage systems

The advent of the smart grid requires both reliable, cost-effective energy storage solutions and the ability to accurately and efficiently simulate these systems. Thermocline thermal energy storage, where heat is stored over a temperature gradient, is a promising energy storage technology. However, because of the complexities of thermal stratification, accurate, yet simple models are difficult to identify and generally require complex computational fluid dynamics (CFD) models. In this work, a novel, adaptive-grid one-dimensional model for representing thermocline thermal energy storage systems is presented and validated using experimental data. Compared to standard, fixed-grid one-dimensional models, the adaptive-grid model improves accuracy and decreases the required number of state variables and equations by using a high-resolution grid in the region of thermal stratification and larger, variable-volume, isothermal nodes to represent the ends of the tank. Experimental data shows that the adaptive-grid model is more accurate than other one-dimensional models because it minimizes the effect of numerical diffusion and better predicts system behavior when temperature inversion is introduced into the system. The model presented has applicability in both cold and hot thermal energy storage systems and is advantageous over CFD models when many repeated simulations are required, such as in optimization, control, or prediction of long-term performance.

Higher order cell-based multidimensional upwind schemes for flow in porous media on unstructured grids

Standard reservoir simulation schemes employ single-point upstream weighting for convective flux approximation. These schemes introduce both coordinate-line numerical diffusion and cross-wind diffusion into the solution that is grid and geometry dependent.New locally conservative cell-based multi-dimensional upwind schemes and higher-order cell-based multi-dimensional upwind schemes that reduce both directional and cross-wind diffusion are presented for convective flow approximation. The new higher-order schemes are comprised of two steps; (a) Higher-order approximation that corrects the directional diffusion of the approximation. (b) Truly multi-dimensional upwind approximation, which involves flux approximation using upwind information obtained by upstream tracing along multi-dimensional flow paths. This approximation reduces cross-wind diffusion. Conditions on tracing direction and CFL number lead to a local maximum principle that ensures stable solutions free of spurious oscillations. The schemes are coupled with full-tensor Darcy flux approximations.Benefits of the resulting schemes are demonstrated for classical convective test cases in reservoir simulation including cases with full tensor permeability fields, where the methods prove to be particularly effective. The test cases involve a range of unstructured grids with variations in orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The higher dimensional formulations are shown to effectively reduce numerical cross-wind diffusion effects, leading to improved resolution of concentration and saturation fronts.

IRIS: a generic three-dimensional radiative transfer code

We present IRIS, a new generic three-dimensional (3D) spectral radiative transfer code that generates synthetic spectra, or images. It can be used as a diagnostic tool for comparison with astrophysical observations or laboratory astrophysics experiments. We have developed a 3D short-characteristic solver that works with a 3D nonuniform Cartesian grid. We have implemented a piecewise cubic, locally monotonic, interpolation technique that dramatically reduces the numerical diffusion effect. The code takes into account the velocity gradient effect resulting in gradual Doppler shifts of photon frequencies and subsequent alterations of spectral line profiles. It can also handle periodic boundary conditions. This first version of the code assumes Local Thermodynamic Equilibrium (LTE) and no scattering. The opacities and source functions are specified by the user. In the near future, the capabilities of IRIS will be extended to allow for non-LTE and scattering modeling. IRIS has been validated through a number of tests. We provide the results for the most relevant ones, in particular a searchlight beam test, a comparison with a 1D plane-parallel model, and a test of the velocity gradient effect. IRIS is a generic code to address a wide variety of astrophysical issues applied to different objects or structures, such as accretion shocks, jets in young stellar objects, stellar atmospheres, exoplanet atmospheres, accretion disks, rotating stellar winds, cosmological structures. It can also be applied to model laboratory astrophysics experiments, such as radiative shocks produced with high power lasers.

Cell culture using centrifugal microfluidic platform with demonstration on Pichia pastoris

This paper discusses the vortical flow, mixing and cell culture of Pichia pastoris using a centrifugal microfluidic (CM) chamber. The resultant "spiral toroidal vortex" in the chamber is made up of a primary vortex induced from inertial acceleration/deceleration of the chamber superposed by a secondary toroidal vortex due to Coriolis acceleration acting on the primary vortex. A validated numerical fluid-flow model with minimized numerical diffusion effect has been developed to investigate the flow and consequently mixing of two-color liquids through cyclic constant acceleration-and-deceleration in the same rotation direction until homogeneous mixing of the two liquids in the CM chamber has been established. The specific mixing time is found to improve with increase in acceleration/deceleration and angular span of the chamber. An experimental CM platform with three cell-culture chambers of different angular spans has been built and Pichia pastoris cell culture has been successfully demonstrated. Cell growth can be monitored over time on the extracted samples by measuring the optical density at 600-nm wave-length. Comparing with conventional cell culture, Pichia pastoris cultured on CM platform exhibits a very short lag (cell preparation/budding) phase prior to the log phase (cell growth). While it takes 8 to 12 h for the conventional shake flask in the lag phase, it takes only 2 h for the CM platform irrespective of initial cell concentration (8.1 × 10(4) to 8.1 × 10(5)/ml), acceleration/deceleration (10 to 32/s(2)) and angular span of the culture chamber (π/12 to π/4), representing significant time reduction. This is largely attributed to better growth conditions due to enhanced mixing and appropriate shear-stress stimulation from the efficient spiral toroidal vortex.