Required Time Steps Research Articles

Transforming chaotic and stiff systems to improve numerical accuracy

AbstractSystems of differential equations can exhibit chaotic or stiff behavior under specific conditions, posing challenges for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution for specified accuracy. In order to improve efficiency, the question arises whether transformation to asymptotically stable solutions can be performed, for which neighbouring solutions converge towards each other at a controlled rate. Employing the concept of local Lyapunov exponents, it is shown that chaotic differential equations can indeed be transformed to obtain high accuracy, whereas stiff equations cannot. For instance, the accuracy of explicit fourth order Runge–Kutta solution of the Lorenz chaotic equations can be increased by several orders of magnitude. Alternatively, the time step can be significantly extended with retained accuracy. The transform method applies broadly to chaotic systems, including weather prediction and turbulence.

Experimental, analytical, and numerical quantification of the Marangoni effect in static refractory finger test

This study investigated the local corrosion of alumina and magnesia refractory in CaO–Al2O3–SiO2–MgO slag due to the Marangoni effect, which is a key factor for localized wear in different industrial processes, using experimental, analytical, and numerical approaches. The objective is to explore the Marangoni effect using computational fluid dynamics simulation aiming to provide insights into the dominant slag flow patterns influencing refractory corrosion and to determine whether the observed corrosion groove can be attributed solely to the Marangoni effect. Static finger tests were conducted at temperatures of 1500 and 1550 °C employing a continuous wear testing device. A two-dimensional axisymmetrical section model of the test assembly was created, incorporating concentration-dependent surface tension gradients and surface tension forces to replicate the Marangoni flow. As the surface-tension simulation required time steps in the order of 10−5 s, modeling up to the experimental time scale cannot be realized. Consequently, the simulation outcomes were extrapolated to anticipate the groove radii of the experimental corrosion steps. Corrosion rates were derived from measurements and analytical methodologies. Established analytical equations for corrosion under surface-tension-flows were adapted to enhance the accuracy of corrosion rate estimation. However, the analytical considerations yielded poor estimates. Meanwhile, the employed simulation model successfully generated plausible predictions of the Marangoni flow. Drawing from the extrapolated simulation outcomes, the projected groove radii exhibited a close correspondence to the measured values, demonstrating a relative error of approximately 3 %, 11 %, and 15 % for the magnesia system at 1500 °C and alumina systems at 1500 and 1550 °C, respectively. Taking into account the uncertainties inherent in the methodological approach, the disparities in the alumina values suggest the involvement of mechanisms beyond the Marangoni effect in the localized wear. Consequently, this study effectively clarifies the impact of the Marangoni effect on the local wear of the examined material systems.

Study on the moving cross‐hatched textures under starved lubrication based on parallel calculation

AbstractThe oil storage effect of textures is beneficial for lubrication performance under starved lubrication. When the larger of the two surfaces in friction pairs is textured, the moving textures should be considered because the boundary conditions are transiently changed at each moment. This is especially for the cross‐hatched textures, which are manufactured on the cylinder liner while not on the piston ring. However, it means that the calculation cost will be very expensive for engineering friction pairs because the required calculation scale is very large and the required time step is very small. So the dynamic characteristics of moving textures on engineering surfaces are normally neglected in the existing researches. In this study, a starved lubrication model of the piston ring‐cylinder liner (PRCL) system is established considering the oil storage effect, local hydrodynamic effect and dynamic characteristics of the moving cross‐hatched textures. To speed up the calculation, an efficient parallel algorithm is developed. The results show that there is a significant difference in minimum oil film thickness (MOFT), wear load and oil film boundaries between stationary textures and moving textures, so the moving textures should not be simplified. This is helpful to find a better design of textures for engineering friction pairs.

Partially explicit time discretization for nonlinear time fractional diffusion equations

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses a coarse spatial grid for spatial resolution. For temporal discretization, implicit methods are often used. For implicit methods, though the time step can be relatively large, the equations are difficult to compute due to the nonlinearity and the fact that one deals with large-scale systems. On the other hand, the discrete systems in explicit methods are easier to compute but it requires small time steps. In this work, we propose a partially explicit scheme following earlier works on developing partially explicit methods for nonlinear diffusion equations. In these schemes, the diffusion term is treated partially explicitly and the reaction term is treated fully explicitly. With the appropriate construction of spaces and stability analysis, we find that the required time step in our proposed scheme scales as the coarse mesh size, which creates a computational saving. The main novelty of this work is the extension of our earlier works for diffusion equations to time fractional diffusion equations. For the case of fractional diffusion equations, the constraints on time steps are more severe and the proposed methods alleviate this problem since the time step in the partially explicit method scales as the coarse mesh size. We present stability analysis. Numerical results are presented where we compare our proposed partially explicit methods with a fully implicit approach. We show that our proposed approach provides similar results while treating many degrees of freedom in nonlinear terms explicitly.

Simulation-Assisted Determination of the Start-Up Time of a Polymer Electrolyte Fuel Cell

Fuel starvation is a major cause of anode corrosion in low temperature polymer electrolyte fuel cells. The fuel cell start-up is a critical step, as hydrogen may not yet be evenly distributed in the active area, leading to local starvation. The present work investigates the hydrogen distribution and risk for starvation during start-up and after nitrogen purge by extending an existing computational fluid dynamic model to capture transient behavior. The results of the numerical model are compared with detailed experimental analysis on a 25 cm2 triple serpentine flow field with good agreement in all aspects and a required time step size of 1 s. This is two to three orders of magnitude larger than the time steps used by other works, resulting in reasonably quick calculation times (e.g., 3 min calculation time for 1 s of experimental testing time using a 2 million element mesh).

Karst modelling challenge 1: Results of hydrological modelling

The complexity of karst groundwater flow modelling is reflected by the amount of simulation approaches. The goal of the Karst Modelling Challenge (KMC) is comparing different approaches on one single system using the same data set. Thirteen teams with different computational models for simulating discharge variations at karst springs have applied their respective models on one single data set coming from the Milandre Karst Hydrogeological System (MKHS). The approaches include neural networks, reservoir models, semi-distributed models and fully distributed groundwater models. Four and a half years of hourly or daily meteorological input and hourly discharge data were provided for model calibration. The validation comprised forecasting one year of discharge, without the observed discharge data. The model performance was evaluated using the volume conservation, Nash-Sutcliffe efficiency (NSE) and the Kling-Gupta efficiency (KGE) applied on the total discharge and individual flow components. As a result, the comparison of model performances is a challenging task due to the differences in the model architecture but also required time steps: some of the models require aggregated daily steps while others could be run using hourly data, which provided some interesting differences depending on how the data was transformed. The use of instantaneous data (e.g. value at noon) produces less bias that averaging hourly data over one day. The transformation of hourly into daily data produces a decrease of Nash and KGE of 0.05 to 0.08 (i.e. from 1 to ~0.93). The resulting simulations (forecasted values for year 2016) produced KGEs ranging between 0.83 and 0.37 (0.83 to −0.24 for NSE). Although the simulations matched the monitored flows reasonably well, most models struggled to simulate baseflow conditions accurately. In general, the models that performed the best for this exercise were the global ones (Gardenia and Varkarst), with a limited number of parameters, which can be calibrated using automatic calibration procedures. The neural network models also showed a fair potential, with one providing reasonable results despite the relatively short dataset available for warming-up (4.5 years). Semi-and fully distributed models also suggested that with some more effort they could perform well. The accuracy of model predictions does not seem to increase by using models with more than 9–12 calibration parameters. An evaluation of the relative errors between the forecasted and the observed values revealed that for most models, 50% of the forecasted values contained more than 50% of difference against the observed discharge rate, with 25% having a difference larger than 100%. A significant part of the poorly forecasted values corresponded to base-flow which was surprising given that as base-flow is generally much easier to predict than peak flow. Hence, this shows that modelling approaches and criteria for the calibration are too oriented towards peak-flow sections of the hydrographs, and that improvements could be gained by more focus on the base-flow.

Extended Lattice Boltzmann Model.

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

Catchment-scale multi-process modeling with local time stepping

Numerical modeling is an important tool for prediction, analysis and understanding of the dynamics of land surface processes. To increase the usage and impact of such tools, it is crucial to decrease runtime by increasing computational efficiency. Dynamic processes such as water flow are typically described by higher-order differential equations. Solving these accurately requires numerical integration over time, where numerical errors depend on the time steps taken. Typically, flow simulation use the smallest required time steps in a model’s domain to simulate flow. In this paper, we analyze the usage of local time stepping, for catchment-scale simulation of land surface processes such as water flow, infiltration, slope stability and landslide runout. In such a scheme, temporal integration is cell specific, allowing for higher numerical efficiency. The implemented scheme works with fully free local time steps that are synchronized only for visualization. We implement this method in a monotonic upwind scheme for conservation laws (MUSCL). We investigate the influence on stability and the resulting changes in computation time and accuracy in a hydrology-coupled, catchment-scale flood simulation. Results show that local time stepping can be implemented in a total variation diminishing (TVD) numerical scheme that is second-order spatially accurate. Simulation results in both 1D dam-break scenarios and catchment-scale flash flood scenarios show insignificant changes in modeling result, while computation time reduces with over 50%. Finally, the method is successfully implemented in a multi-process lands surface model with hydrology, flooding, slope failure, and runout. The implementation of a local time stepping for computation of dynamic land surface processes could be implemented widely for increased computational efficiency without significant loss of accuracy.

Neural-network interatomic potential for grain boundary structures and their energetics in silicon

Artificial neural-network (ANN) interatomic potentials for simulating atomic structures and energetics of grain boundaries (GBs) in silicon were constructed and integrated into structural optimization and molecular dynamics (MD) algorithms. A training dataset including various atomic environments of symmetric tilt GBs was generated by performing density-functional-theory (DFT) calculations. The ANN potential after training was found to be capable of approximating the potential-energy surface at GBs even with dangling bonds and large atomic displacements at high temperatures, which cannot be well reproduced with empirical interatomic potentials. Additionally, reliability of the ANN potential for molecular simulations was evaluated. GB structures optimized or equilibrated by the ANN molecular simulations were also energetically lower for DFT calculations, without significant errors. The ANN potential is therefore expected to greatly reduce structural-optimization iterations and required time steps to acquire stable or equilibrium GB structures in MD simulations, enabling us to address even large-scale systems of general GBs in silicon, with high accuracy and low computational cost.

Explicit Nonlinear Model Predictive Control for Electric Vehicle Traction Control

This paper presents a traction control (TC) system for electric vehicles with in-wheel motors, based on explicit nonlinear model predictive control. The feedback law, available beforehand, is described in detail, together with its variation for different plant conditions. The explicit controller is implemented on a rapid control prototyping unit, which proves the real-time capability of the strategy, with computing times on the order of microseconds. These are significantly lower than the required time step for a TC application. Hence, the explicit model predictive controller can run at the same frequency as a simple TC system based on proportional integral (PI) technology. High-fidelity model simulations provide: 1) a performance comparison of the proposed explicit nonlinear model predictive controller (NMPC) with a benchmark PI-based traction controller with gain scheduling and anti-windup features, and 2) a performance comparison among two explicit and one implicit NMPCs based on different internal models, with and without consideration of transient tire behavior and load transfers. Experimental test results on an electric vehicle demonstrator are shown for one of the explicit NMPC formulations.

Multiphysics Modeling of Voice Coil Actuators With Recurrent Neural Network

In order to accurately model the behaviors of a voice coil actuator (VCA), the three-dimensional (3-D) method is preferred over a lumped model. However, building a 3-D model of a VCA is often very computationally expensive. The computation efficiency can be limited by the spatial discretization, the multiphysics nature, and the nonlinearities of the VCA. In this paper, we propose incorporating the recurrent neural network (RNN) into the multiphysics simulation to enhance its computation efficiency. In the proposed approach, the multiphysics problem is first solved with the finite element method (FEM) at full 3-D accuracy within a portion of the required time steps. An RNN is then trained and validated with the obtained transient solutions. Once the training completes, the RNN can make predictions on the transient behaviors of the VCA in the remaining portion of the required time steps. With the proposed approach, it avoids solving the 3-D multiphysics problem at all time steps such that a significant reduction of computation time can be achieved. The training cost of the RNN model can be amortized when a longer duration of transient behaviors is required. A loudspeaker example is used to demonstrate the enhancement of the computation efficiency by using RNN in the multiphysics modeling. Various structures of neural networks and tunable parameters are investigated with the numerical example in order to optimize the performance of the RNN model.

Numerically accelerated pore-scale equilibrium dissolution

Simulation of dissolution processes with a pore-scale reactive transport model increases insight in coupled chemical-physical-transport processes. However, modelling of dissolution process often requires a large number of time steps especially when the buffering capacity of solid phases is high. In this work we analyze the interplay between solid buffering on one hand and transport on the other. Based on this analysis we propose an approach to reduce the number of required time steps for simulating equilibrium dissolution processes. The underlying idea is that the number of time step iterations can be reduced if the buffering is sufficient to bring the system to a steady state, i.e. that the concentration field around solid is time-invariant. If this condition is satisfied, then it is possible to reduce the physical (and thus also computational) time by adjusting the chemical system appropriately. First we derived a dimensionless value - called buffering number - to determine under which conditions reduction in time can be made. Several examples illustrate that below a certain buffering number, the physical time can be reduced without significant effect on result (e.g. dissolution front) as long as the solid volume fraction is sufficient. This means that for a given solid-liquid system, the calculation time can be reduced either by the reduction of mass in solid or by the increase of equilibrium concentration (solubility). We also show that the calculation time for calcium leaching in cementitious systems can be reduced by 50 times with a negligible error.

Methods for controlling the local spatial and temporal resolution of vortex particle simulations of bluff body aerodynamics problems

This paper presents a novel adaptive solution strategy for vortex particle methods that allows the efficient resolution of multiple scales that are characteristic of flows around bluff bodies with small structural details. The efficiency of the method arises from maintaining a sufficiently high spatial numerical discretisation near the fluid-solid interface and a progressive coarsening away from the bodies and their structural details. The control of the particle map is achieved through remeshing based on high-order interpolation kernels and ensures an accurate representation of the flow features of different scales whose resolution is critical to an accurate computation of the pressures on the immersed structure subjected to separated flows. As the required time step of the time integration is directly related to the spatial resolution, the adaptivity is further enhanced by a temporal adaptivity realized through a sub-stepping technique for controlling the frequency at which the particle convection and diffusion steps are performed. The validation of the proposed technique is performed by simulations of the impulsively started flow past a circular cylinder at Reynolds number 3000, where both the spatial and the temporal strategies are at first independently studied and then combined to full adaptivity. A substantially higher computational efficiency compared to equally accurate non-adaptive simulations is reported. Further studies of accuracy and efficiency are performed by simulating the flow past the cross section of a bridge arch geometry featuring small structural details. Solution properties studied include the resolution of local velocity profiles and global aerodynamic coefficients. These reveal how the application of the full adaptive strategy enables for the accurate and efficient prediction of the flow features. The results indicate speed-ups of up to factor 4 to 5 when comparing the new approach to the classical Vortex Particle Method.

Time-dependent restricted-active-space self-consistent-field theory with space partition

Aiming at efficient numerical analysis of time-dependent (TD) many-electron dynamics of atoms involving multielectron continua, the TD restricted-active-space self-consistent-field theory with space partition (TD-RASSCF-SP) is presented. The TD-RASSCF-SP wave function is expanded in terms of TD configuration-interaction coefficients with Slater determinants composed of two kinds of TD orbitals: $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ orbitals are defined to be nonvanishing in the inner region ($\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{V}$), a small volume around the atomic nucleus, and $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{M}$ orbitals are nonvanishing in the large outer region ($\stackrel{\ifmmode \check{}\else \v{}\fi{}}{V}$). For detailed discussion of the SP strategy, the equations of motion are derived by two different formalisms for comparison. To ensure continuous differentiability of the wave function across the two regions, one of the formalisms makes use of the property of the finite-element discrete-variable-representation (FEDVR) functions and introduces additional time-independent orbitals. The other formalism is more general and is based on the Bloch operator as in the $R$-matrix theory, but turns out to be less practical for numerical applications. Hence, using the FEDVR-based formalism, the numerical performance is tested by computing double-ionization dynamics of atomic beryllium in intense light fields. To achieve high accuracy, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ should be set large to take into account the strong many-electron correlation around the nucleus. On the other hand, $\stackrel{\ifmmode \check{}\else \v{}\fi{}}{M}$ can be set much smaller than $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ for capturing the weaker correlation between the two outgoing photoelectrons. As a result, compared with more accurate multiconfigurational TD Hartree-Fock (MCTDHF) method, the TD-RASSCF-SP method may achieve comparable accuracy in the description of the double-ionization dynamics. There are, however, difficulties related to the stiffness of the equations of motion of the TD-RASSCF-SP method, which makes the required time step for this method smaller than the one needed for the MCTDHF approach.

Model-based review of Doppler global velocimetry techniques with laser frequency modulation

Optical measurements of flow velocity fields are of crucial importance to understand the behavior of complex flow. One flow field measurement technique is Doppler global velocimetry (DGV). A large variety of different DGV approaches exist, e.g., applying different kinds of laser frequency modulation. In order to investigate the measurement capabilities especially of the newer DGV approaches with laser frequency modulation, a model-based review of all DGV measurement principles is performed. The DGV principles can be categorized by the respective number of required time steps. The systematic review of all DGV principle reveals drawbacks and benefits of the different measurement approaches with respect to the temporal resolution, the spatial resolution and the measurement range. Furthermore, the Cramér-Rao bound for photon shot is calculated and discussed, which represents a fundamental limit of the achievable measurement uncertainty. As a result, all DGV techniques provide similar minimal uncertainty limits. With Nphotons as the number of scattered photons, the minimal standard deviation of the flow velocity reads about 106m/s/Nphotons, which was calculated for a perpendicular arrangement of the illumination and observation direction and a laser wavelength of 895nm. As a further result, the signal processing efficiencies are determined with a Monte-Carlo simulation. Except for the newest correlation-based DGV method, the signal processing algorithms are already optimal or near the optimum. Finally, the different DGV approaches are compared regarding errors due to temporal variations of the scattered light intensity and the flow velocity. The influence of a linear variation of the scattered light intensity can be reduced by maximizing the number of time steps, because this means to acquire more information for the correction of this systematic effect. However, more time steps can result in a flow velocity measurement with a lower temporal resolution, when operating at the maximal frame rate of the camera. DGV without laser frequency modulation then provides the highest temporal resolutions and is not sensitive with respect to temporal variations but with respect to spatial variations of the scattered light intensity. In contrast to this, all DGV variants suffer from velocity variations during the measurement. In summary, the experimental conditions and the measurement task finally decide about the ideal choice from the reviewed DGV methods.

Coarse-scale particle tracking approaches for contaminant transport in fractured rock

Random-walk particle tracking methods are frequently used for modeling contaminant transport, as relevant to radionuclide transport in fractured rock. Standard particle-tracking methods need to be modified for handling discontinuities in velocity and diffusion coefficients as at fracture–matrix interfaces, and handling these discontinuities accurately requires time steps much smaller than the diffusion time scale across narrow fracture apertures. In this work we present coarse-scale particle tracking methods that exploit the contrast in diffusivities between fracture and rock matrix to allow the use of time steps much larger than the diffusion time scale across fracture apertures. Thus, they reduce computational effort by several orders of magnitude. We develop two coarse-scale versions of the standard particle tracking method, one applicable to particles starting in the fracture, and another to particles starting in the rock matrix. The two methods can be used in combination to track particles through individual fractures, including the influence of matrix diffusion. The main advantage of our methods result from the computationally efficient treatment of (two-way) fracture–matrix particle transfer. These methods can also be combined with existing particle tracking approaches for complex advection–diffusion–dispersion in fractures to handle fracture–matrix interactions efficiently.

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the $K_\alpha$ sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.

Dimension reduction numerical closure method for advection–diffusion-reaction systems

Many natural physical processes allow different mathematical descriptions on different scales. The microscale description is usually based on fundamental conservation laws that form a closed system of ordinary differential equations (ODEs) or partial differential equations (PDEs) but the numerical discretization of these equations may produce a system of ODEs with an enormous number of unknowns. Furthermore, time integration of the microscale equations usually requires time steps that are smaller than the observation time by many orders of magnitude. A direct solution of these ODEs can be extremely expensive. Often, we are only interested in the average behavior of the microscale system rather than the exact solution of the ODEs. Here we propose a novel dimension reduction computational closure (DRNC) method that gives an approximate solution of the ODEs and provides an accurate prediction of the average behavior. The DRNC method consists of two main elements. First, effective ODEs for evolution of average variables (e.g. average velocity, concentration and mass of a mineral precipitate) are obtained by averaging the micro-scale ODEs over the entire micro-scale domain. These effective ODEs contain non-local terms in the form of volume integrals of functions of the micro-scale variables. Second, a numerical closure is used to close the system of the effective equations. The numerical closure is achieved via short bursts of the microscale model. The DRNC method is used to simulate flow and transport with mixing controlled reactions and mineral precipitation by reducing porescale (microscale) Navier–Stokes and advection–diffusion-reaction equations to ODEs for averaged velocity and concentrations. Good agreement between direct solutions of the microscale equations and DRNC solutions for different boundary conditions and Damkohler numbers confirms the accuracy and computational efficiency of DRNC method. The DRNC method significantly accelerates microscale simulations, while providing accurate approximation of the microscale solution and accurate prediction of the average behavior of the system.

A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift–diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift–diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods.

Development of Sub-Daily Erosion and Sediment Transport Algorithms for SWAT

New Soil and Water Assessment Tool (SWAT) algorithms for simulation of stormwater best management practices (BMPs) such as detention basins, wet ponds, sedimentation filtration ponds, and retention irrigation systems are under development for modeling small/urban watersheds. Modeling stormwater BMPs often requires time steps as small as minutes to realistically capture the instantaneous flow and sediment load coming from upland areas. SWAT2005 uses the Modified Universal Soil Loss Equation (MUSLE) for modeling upland erosion and sediment load. The MUSLE model is an empirical soil loss equation, which was formulated based on field observations rather than theoretically derived relationships to predict long-term average soil loss. This article presents modified physically based erosion models in SWAT for seamless modeling of erosion processes with the recently developed sub-hourly flow models. In the new algorithms, splash erosion is calculated based on the kinetic energy delivered by raindrops, adapted from the European Soil Erosion Model, and overland flow erosion is estimated using a physically based equation adapted from the Areal Nonpoint-Source Watershed Environment Response Simulation (ANSWERS) model. The Yang model and the Brownlie model were also modified for in-stream sediment routing. The SWAT model with the modified sub-daily sediment algorithms was calibrated and validated each for a one-year period at 15 min intervals with measured data from the USDA-ARS Riesel watersheds in Texas. Results show that SWAT with the sub-daily algorithms performed as well or better in terms of sediment yield prediction than SWAT with the current daily output structure. In addition, SWAT (sub-daily) was able to adequately represent the timing, peak, and duration of sediment transport events. Thus, this initial evaluation indicates that the new sub-daily flow and sediment structure in SWAT is a promising tool for water quality assessment studies in small watersheds or urban watersheds where sub-daily process are so important to quantify.