Nodal Domain Integration Research Articles

A two-field semi-Lagrangian reproducing kernel model for impact and penetration simulation into geo-materials

In this paper, a displacement–pressure (u–p) semi-Lagrangian reproducing kernel (RK) is introduced to study the penetration depth of various projectile types into dry and fully saturated geo-materials. To describe the poromechanics of saturated materials, Biot theory is incorporated into the semi-Lagrangian formulation and a damage model is embedded into Drucker–Prager constitutive model to simulate the soil behavior and separation during the impact and penetration process. The stabilized nodal domain integration is developed in the two-field semi-Lagrangian RK formulation to ensure numerical stability, and the kernel contact algorithm is implemented to model the interaction between soil and projectile bodies. Several examples are studied to validate and assess the proposed method’s performance in predicting the final penetration depth, and the results are compared to those reported in the literature.

Groundwater quality management of a low inertia basin: Application to the San Mateo Basin, California

A two-dimensional finite element model is applied to the San Mateo Basin, California in order to investigate feasible and efficient management alternatives to enhance the basin yield and preserve the basin water quality. The model utilizes lumped approximation methods for the determination of its subsurface boundary conditions, and incorporates a variety of hydrological processes. The model solves uncoupled flow and transport equations using a nodal domain integration technique for the flow model and an integrated finite difference method for the transport model. The model incorporates the basin inputs and outputs as ocean flux, well and phreatophyte extractions, subsurface inflow, precipitation and streambed percolation. Modeling results indicate that the substained yield may be maximized by interception of ocean outflow from the basin. An improvement of about four times of the historical sustained yield was achieved. This strategy required relocation of existing wastewater recharge ponds and increasing basin extractions. In order to intercept most of the ocean outflow by increasing basin extractions, simulated subsurface seawater intrusion was observed. The water quality study indicated that the basin yield could be increased significantly by moderately relaxing the water quality criteria near the ocean.

A UNIFIED MODEL OF RADIALLY SYMMETRIC HEAT CONDUCTION

The nodal domain integration method is applied to a radially symmetric heat conduction problem where the solution domain is discretized into irregular radial finite elements, and the state variable is approximated by a spatial linear trial function within each finite element. The resulting finite-element model represents the well-known Galerkin finite-element, subdomain-integration, and an integrated finite-difference numerical statement as well as an infinity of other mass-lumped matrix schemes. From the NDI approach, the several numerical modeling techniques are unified into one global domain model where each submodel can be obtained by the specification of a single mass-lumping parameter.

Two-Dimensional Model of Coupled Heat and Moisture Transport in Frost-Heaving Soils

A two-dimensional model of coupled heat and moisture flow in frost-heaving soils is developed based upon well known equations of heat and moisture flow in soils. Numerical solution is by the nodal domain integration method which includes the integrated finite difference and the Galerkin finite element methods. Solution of the phase change process is approximated by an isothermal approach and phenomenological equations are assumed for processes occurring in freezing or thawing zones. The model has been verified against experimental one-dimensional freezing soil column data and experimental two-dimensional soil thawing tank data as well as two-dimensional soil seepage data. The model has been applied to several simple but useful field problems such as roadway embankment freezing and frost heaving.

Nodal domain integration model of two-dimensional advection-diffusion processes

The nodal domain integration method is applied to a two-dimensional advection-diffusion process in an anisotropic inhomogeneous medium. The domain is discretised into the union of irregular triangle finite elements with vertex-located nodal points and a linear trial function is used to approximate the governing flow equation's state variable in each element. Non-linear parameters are assumed quasi-constant for small durations in time in each element. The resulting numerical model represents the Galerkin and subdomain integration weighted residual methods and the integrated finite difference method as special cases. Both Dirichlet and Neumann boundary conditions are accommodated in a manner similar to the Galerkin finite element approach.

MASS-LUMPING NUMERICAL MODELS OF THREE-DIMENSIONAL HEAT CONDUCTION

Abstract A variable mass-lumping numerical model (nodal domain integration) of three-dimensional heat conduction in an inhomogeneous continuum is developed The domain is discretized by tetrahedron-shaped elements and the state variable is approximated by linear trial functions. The resulting model represents the Galerkin finite-element, subdomain intergration, and integrated finite-difference methods as special cases and accommodates both Dirichlet and Neumann boundary conditions similar to a Galerkin finite-element model Consequently, a unified domain numerical model is developed that readily represents each of the abovementioned domain numerical methods and an infinity of finite-element mass-lumping schemes by the specification of a single constant model parameter. Application of the nodal domain integration model to linear heat conduction problems indicates that the degree of model mass lumping must vary to minimize the approximation error.

Mass lumping models of the linear diffusion equation

The nodal domain integration method is used to develop a numerical model of the linear diffusion equation. The nodal domain integration approach is shown to represent an infinity of finite element mass matrix lumping schemes including the Galerkin and subdomain integration versions of the weighted residual method and an integrated finite difference method. Neumann, Dirichlet and mixed boundary conditions are accommodated analogous to the Galerkin finite element method. In order to reduce the overall integrated approximation relative error, a mass matrix lumping formulation is developed which is based on the Crank-Nicolson time advancement approximation. The optimum mass lumping factors are found to be strongly related to the model timestep size.

Correction to ‘Nodal domain integration model of unsaturated two‐dimensional soil‐water flow: Development’

Water Resources ResearchVolume 18, Issue 2 p. 447-447 CorrectionsFree Access Correction to ‘Nodal domain integration model of unsaturated two-dimensional soil-water flow: Development’ T. V. Hromadka II, T. V. Hromadka IISearch for more papers by this authorG. L. Guymon, G. L. GuymonSearch for more papers by this authorG. C. Pardoen, G. C. PardoenSearch for more papers by this author T. V. Hromadka II, T. V. Hromadka IISearch for more papers by this authorG. L. Guymon, G. L. GuymonSearch for more papers by this authorG. C. Pardoen, G. C. PardoenSearch for more papers by this author First published: April 1982 https://doi.org/10.1029/WR018i002p00447AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume18, Issue2April 1982Pages 447-447 RelatedInformation

Nodal domain integration model of one-dimensional advection—diffusion

The nodal domain integration method is applied to a one-dimensional advection—diffusion mathematical model without a source term. Comparison of the resulting numerical model to the well known Galerkin finite element, subdomain, and finite difference domain models indicates that a single numerical statement can be developed which includes the Galerkin finite element, subdomain, and finite difference models as special cases.

Nodal domain integration model of unsaturated two‐dimensional soil‐water flow: Development

The nodal domain integration method is applied to a two‐dimensional unsaturated soil water flow problem where the solution domain is discretized into irregular triangular elements and the state variable is approximated by a spatial linear trial function within each triangular element. The resulting element matrices incorporate the well‐known Galerkin finite element, subdomain, and integrated finite difference numerical statements as special cases of the nodal domain integration numerical statement.

Improved linear trial function finite element model of soil moisture transport

Two methods of modeling a higher‐order approximation function of soil moisture transport by an improved linear trial function approximation are presented. The first approach considered is based upon use of the alternation theorem and a finite element capacitance matrix that incorporates the Galerkin finite element, subdomain, finite difference, and proposed nodal domain integration methods. The second approach extends the first approach by developing a temporal relationship for element matrices such that a higher‐order approximation function can be modeled by a linear approximation function. Comparison of model results produced from a nodal domain integration model incorporating these improved linear trial function approximations to the finite element, subdomain, and finite difference methods indicates that this approach may lead to a generalized modeling method for soil moisture transport problems.