scholarly journals A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid

Geosciences ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 257
Author(s):  
Jingyu Gao ◽  
Maxim Smirnov ◽  
Maria Smirnova ◽  
Gary Egbert
Keyword(s):  
Forward Modeling ◽  
Horizontal Resolution ◽  
Initial Guess ◽  
Explicit Scheme ◽  
Implicit Scheme ◽  
Time Step ◽  
Forward Solution ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Background Models

This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. We developed time-domain finite-difference modeling based on the explicit scheme earlier. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. Instead, we test various initial guesses based on the linear extrapolation or linear combination of the solutions from several previous steps. We build up the implicit scheme forward modeling on the multi-resolution grid, which allows for the adjustment of the horizontal resolution with depth, hence improving the performance of the forward operator. Synthetic examples show the implicit scheme forward modeling using the linearly combined initial guess estimate on the multi-resolution grid additionally reduces the run time compared to the standard initial guess approach. The result of comparison between the implicit scheme developed here with the previously developed explicit scheme shows that the explicit scheme modeling is more efficient for more conductive background models often found in environmental studies. However, the implicit scheme modeling is more suitable for the simulation with highly resistive background models, usually occurring in mineral exploration scenarios. Thus, the inverse problem can be solved using more efficient forward solution depending on the modeling setup and background resistivity.

Multipoint Explicit Differencing (MED) for Time Integrations of the Wave Equation

2007 ◽  
Vol 135 (11) ◽  
pp. 3862-3875 ◽  
Author(s):  
Celal S. Konor ◽  
Akio Arakawa
Keyword(s):  
Wave Equation ◽  
Finite Number ◽  
Multilevel Models ◽  
Horizontal Resolution ◽  
Explicit Scheme ◽  
Implicit Scheme ◽  
Courant Number ◽  
Time Step ◽  
Wide Range ◽  
Grid Points

Abstract For time integrations of the wave equation, it is desirable to use a scheme that is stable over a wide range of the Courant number. Implicit schemes are examples of such schemes, but they do that job at the expense of global calculation, which becomes an increasingly serious burden as the horizontal resolution becomes higher while covering a large horizontal domain. If what an implicit scheme does from the point of view of explicit differencing is looked at, it is a multipoint scheme that requires information at all grid points in space. Physically this is an overly demanding requirement because wave propagation in the real atmosphere has a finite speed. The purpose of this study is to seek the feasibility of constructing an explicit scheme that does essentially the same job as an implicit scheme with a finite number of grid points in space. In this paper, a space-centered trapezoidal implicit scheme is used as the target scheme as an example. It is shown that an explicit space-centered scheme with forward time differencing using an infinite number of grid points in space can be made equivalent to the trapezoidal implicit scheme. To avoid global calculation, a truncated version of the scheme is then introduced that only uses a finite number of grid points while maintaining stability. This approach of constructing a stable explicit scheme is called multipoint explicit differencing (MED). It is shown that the coefficients in an MED scheme can be numerically determined by single-time-step integrations of the target scheme. With this procedure, it is rather straightforward to construct an MED scheme for an arbitrarily shaped grid and/or boundaries. In an MED scheme, the number of grid points necessary to maintain stability and, therefore, the CPU time needed for each time step increase as the Courant number increases. Because of this overhead, the MED scheme with a large time step can be more efficient than a usual explicit scheme with a smaller time step only for complex multilevel models with detailed physics. The efficiency of an MED scheme also depends on how the advantage of parallel computing is taken.

A New Data-Driven ATHLET – ANSYS CFD Coupling Method for Efficient Simulation of Nuclear Power Plant Circuits

2014 ◽  
Author(s):  
Georgios Theodoridis ◽  
Angel Papukchiev ◽  
Dominik Scholz ◽  
Georg Lerchl
Keyword(s):  
Nuclear Power ◽  
Explicit Scheme ◽  
Implicit Scheme ◽  
Coupling Method ◽  
Data Driven ◽  
Time Step ◽  
Two Phase ◽  
New Approach ◽  
Ansys Cfx ◽  
Coupling Variables

A new data-driven coupling method between the system code ATHLET and ANSYS CFX was developed. The new approach allows for coupled simulations of single and two-phase flow with heat transfer and transport of tracer concentration. Any number of coupling interfaces can be defined with the aid of a graphical user interface. Two coupling schemes have been implemented: an explicit scheme where the coupling variables are exchanged at the end of each CFD time step and a semi-implicit scheme in which the variable exchange is performed for each iteration within each time step. The coupling method was validated with measured data from a single-phase double T-junction mixing experiment. The results of the coupled simulation for the double T-junction case, where 3-D effects are very important, were found in excellent agreement with the experimental data. The semi-implicit scheme was found numerically more accurate and stable than the explicit scheme.

3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. F115-F126 ◽  
Author(s):  
Evan Schankee Um ◽  
Jerry M. Harris ◽  
David L. Alumbaugh
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Electric Field ◽  
Time Domain ◽  
Dirichlet Boundary Conditions ◽  
Earth Model ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Diffusion Phenomena

We present a finite-element time-domain (FETD) approach for the simulation of 3D electromagnetic (EM) diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magnetic fields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields, the electric field diffusion equation is transformed into a system of differential equations via Galerkin’s method with homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-in reduced ordering technique. When advancing the solution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current (FEDC) algorithm that solves Poisson’s equation using a secondary potential method for a general anisotropic earth model. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiency of the 3D FETD algorithm.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

scholarly journals A Unified Convection Scheme (UNICON). Part I: Formulation

2014 ◽  
Vol 71 (11) ◽  
pp. 3902-3930 ◽  
Author(s):  
Sungsu Park
Keyword(s):  
Deep Convection ◽  
Convective Available Potential Energy ◽  
Horizontal Resolution ◽  
Vertical Transport ◽  
Convective Precipitation ◽  
Cold Pool ◽  
Quasi Equilibrium ◽  
Convection Scheme ◽  
Time Step ◽  
Turbulent Eddies

Abstract The author develops a unified convection scheme (UNICON) that parameterizes relative (i.e., with respect to the grid-mean vertical flow) subgrid vertical transport by nonlocal asymmetric turbulent eddies. UNICON is a process-based model of subgrid convective plumes and mesoscale organized flow without relying on any quasi-equilibrium assumptions such as convective available potential energy (CAPE) or convective inhibition (CIN) closures. In combination with a relative subgrid vertical transport scheme by local symmetric turbulent eddies and a grid-scale advection scheme, UNICON simulates vertical transport of water species and conservative scalars without double counting at any horizontal resolution. UNICON simulates all dry–moist, forced–free, and shallow–deep convection within a single framework in a seamless, consistent, and unified way. It diagnoses the vertical profiles of the macrophysics (fractional area, plume radius, and number density) as well as the microphysics (production and evaporation rates of convective precipitation) and the dynamics (mass flux and vertical velocity) of multiple convective updraft and downdraft plumes. UNICON also prognoses subgrid cold pool and mesoscale organized flow within the planetary boundary layer (PBL) that is forced by evaporation of convective precipitation and accompanying convective downdrafts but damped by surface flux and entrainment at the PBL top. The combined subgrid parameterization of diagnostic convective updraft and downdraft plumes, prognostic subgrid mesoscale organized flow, and the feedback among them remedies the weakness of conventional quasi-steady diagnostic plume models—the lack of plume memory across the time step—allowing UNICON to successfully simulate various transitional phenomena associated with convection (e.g., the diurnal cycle of precipitation and the Madden–Julian oscillation).

scholarly journals A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

2021 ◽  
Author(s):  
Chennakesava Kadapa
Keyword(s):  
Wave Propagation ◽  
Wave Speed ◽  
Critical Time ◽  
Incompressible Material ◽  
Implicit Scheme ◽  
Bulk Wave ◽  
Lumped Mass ◽  
Time Step ◽  
Material Models ◽  
Shear Wave Speed

AbstractThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated.

scholarly journals Investigation of Air Pocket Behavior in Pipelines Using Rigid Column Model and Contributions of Time Integration Schemes

Water ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 785
Author(s):  
Arman Rokhzadi ◽  
Musandji Fuamba
Keyword(s):  
Transient Flow ◽  
Time Integration ◽  
Driving Pressure ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Time Step ◽  
Column Model ◽  
Integration Schemes ◽  
Backward Euler

This paper studies the air pressurization problem caused by a partially pressurized transient flow in a reservoir-pipe system. The purpose of this study is to analyze the performance of the rigid column model in predicting the attenuation of the air pressure distribution. In this regard, an analytic formula for the amplitude and frequency will be derived, in which the influential parameters, particularly, the driving pressure and the air and water lengths, on the damping can be seen. The direct effect of the driving pressure and inverse effect of the product of the air and water lengths on the damping will be numerically examined. In addition, these numerical observations will be examined by solving different test cases and by comparing to available experimental data to show that the rigid column model is able to predict the damping. However, due to simplified assumptions associated with the rigid column model, the energy dissipation, as well as the damping, is underestimated. In this regard, using the backward Euler implicit time integration scheme, instead of the classical fourth order explicit Runge–Kutta scheme, will be proposed so that the numerical dissipation of the backward Euler implicit scheme represents the physical dissipation. In addition, a formula will be derived to calculate the appropriate time step size, by which the dissipation of the heat transfer can be compensated.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

scholarly journals Version 2 of the EUMETSAT OSI SAF and ESA CCI Sea Ice Concentration Climate Data Records

2018 ◽  
Author(s):  
Thomas Lavergne ◽  
Atle Macdonald Sørensen ◽  
Stefan Kern ◽  
Rasmus Tonboe ◽  
Dirk Notz ◽  
...  
Keyword(s):  
Sea Ice ◽  
Satellite Data ◽  
Grid Point ◽  
Ice Cover ◽  
Quantitative Information ◽  
Horizontal Resolution ◽  
Climate Data ◽  
Time Step ◽  
Sea Ice Concentration ◽  
Ice Concentration

Abstract. We introduce the OSI-450, the SICCI-25km and the SICCI-50km climate data records of gridded global sea-ice concentration. These three records are derived from passive microwave satellite data and offer three distinct advantages compared to existing records: First, all three records provide quantitative information on uncertainty and possibly applied filtering at every grid point and every time step. Second, they are based on dynamic tie points, which capture the time evolution of surface characteristics of the ice cover and accommodate potential calibration differences between satellite missions. Third, they are produced in the context of sustained services offering committed extension, documentation, traceability, and user support. The three records differ in the underlying satellite data (SMMR & SSM/I & SSMIS or AMSR-E & AMSR2), in the imaging frequency channels (37 GHz and either 6 GHz or 19 GHz), in their horizontal resolution (25 km or 50 km) and in the time period they cover. We introduce the underlying algorithms and provide an initial evaluation. We find that all three records compare well with independent estimates of sea-ice concentration both in regions with very high sea-ice concentration and in regions with very low sea-ice concentration. We hence trust that these records will prove helpful for a better understanding of the evolution of the Earth's sea-ice cover.

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