Research Topic

Meshless Methods for Modeling Transport Phenomena

About this Research Topic

Although many numerical and analytical schemes exist for solving engineering problems, the meshless method is a particularly attractive method that is becoming more widely used in the engineering and scientific modeling communities. Finite difference (FDM), finite volume (FVM), finite element (FEM) and boundary element (BEM) methods have been historically used to model a wide variety of engineering problems in complex geometries that may require extensive meshing. The meshless method is simple, accurate, and requires no meshing. The need to accurately simulate various physical processes in complex geometries is important, and has perplexed modelers utilizing conventional numerical schemes for many years. Today, advances in numerical schemes and enhanced hardware have led to many commercial codes that can employ Herculean efforts to solve complex fluid-thermal and transport phenomena problems. Advances in the development and application of meshless techniques show they can be strong competitors to these classical numerical approaches used to discretize these difficult nonlinear equations.

Meshless methods are uniquely simple, yet provide solution accuracies that can rival FDM, FVM, FEM, and BEM techniques without requiring the need for mesh connectivity. Ease in programming, no domain or surface discretization, no numerical integration, and similar formulations for 2-D and 3-D make meshless methods very attractive. One of the main advantages of meshless methods is that they are computationally easy to add or remove nodes from a preexisting set of nodes. In conventional FDM, FVM, FEM and BEM methods, addition or removal of a point or an element may lead to lengthy remeshing and is usually difficult to implement.

There exist several types of meshless methods, such as kernel methods, moving least square method, partition of unity methods, and radial basis functions. The origin of meshless methods can be traced back to the 1970’s, but very little research was done until the past two decades. Smooth Particle Hydrodynamics is one of the earliest meshless-based methods used for modeling astrophysical phenomena. One of the common characteristics of all the meshfree methods is that a functional approximation or interpolation can be constructed from a set of scattered nodes or points. These methods do not require any storage of prespecified connectivity or relationship among the scattered nodes.

Meshless methods are an attempt to minimize mesh dependence problems in computational methods. The objective is to eliminate mesh dependence by constructing the approximation entirely in terms of nodes. Moving discontinuities and large-scale problems can be resolved more efficiently with comparable accuracy to mesh-based schemes. The nodes can be created in an automated manner without human intervention and time spent in optimizing mesh configurations.

In this Research Topic, we are seeking a set of high quality papers that illustrate and describe the development, application, and recent advancements of meshless methods with emphasis on modeling transport phenomena including heat transfer, fluid flow, and environmental transport topics. Of special interest are papers dealing with Multiphysics interactions, e.g., fluid-structure, fluid-thermal, non-Newtonian flows, species transport, and bioengineering and biomedical applications.


Keywords: Numerical, Meshless, Computational, Fluid, Thermal


Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

Although many numerical and analytical schemes exist for solving engineering problems, the meshless method is a particularly attractive method that is becoming more widely used in the engineering and scientific modeling communities. Finite difference (FDM), finite volume (FVM), finite element (FEM) and boundary element (BEM) methods have been historically used to model a wide variety of engineering problems in complex geometries that may require extensive meshing. The meshless method is simple, accurate, and requires no meshing. The need to accurately simulate various physical processes in complex geometries is important, and has perplexed modelers utilizing conventional numerical schemes for many years. Today, advances in numerical schemes and enhanced hardware have led to many commercial codes that can employ Herculean efforts to solve complex fluid-thermal and transport phenomena problems. Advances in the development and application of meshless techniques show they can be strong competitors to these classical numerical approaches used to discretize these difficult nonlinear equations.

Meshless methods are uniquely simple, yet provide solution accuracies that can rival FDM, FVM, FEM, and BEM techniques without requiring the need for mesh connectivity. Ease in programming, no domain or surface discretization, no numerical integration, and similar formulations for 2-D and 3-D make meshless methods very attractive. One of the main advantages of meshless methods is that they are computationally easy to add or remove nodes from a preexisting set of nodes. In conventional FDM, FVM, FEM and BEM methods, addition or removal of a point or an element may lead to lengthy remeshing and is usually difficult to implement.

There exist several types of meshless methods, such as kernel methods, moving least square method, partition of unity methods, and radial basis functions. The origin of meshless methods can be traced back to the 1970’s, but very little research was done until the past two decades. Smooth Particle Hydrodynamics is one of the earliest meshless-based methods used for modeling astrophysical phenomena. One of the common characteristics of all the meshfree methods is that a functional approximation or interpolation can be constructed from a set of scattered nodes or points. These methods do not require any storage of prespecified connectivity or relationship among the scattered nodes.

Meshless methods are an attempt to minimize mesh dependence problems in computational methods. The objective is to eliminate mesh dependence by constructing the approximation entirely in terms of nodes. Moving discontinuities and large-scale problems can be resolved more efficiently with comparable accuracy to mesh-based schemes. The nodes can be created in an automated manner without human intervention and time spent in optimizing mesh configurations.

In this Research Topic, we are seeking a set of high quality papers that illustrate and describe the development, application, and recent advancements of meshless methods with emphasis on modeling transport phenomena including heat transfer, fluid flow, and environmental transport topics. Of special interest are papers dealing with Multiphysics interactions, e.g., fluid-structure, fluid-thermal, non-Newtonian flows, species transport, and bioengineering and biomedical applications.


Keywords: Numerical, Meshless, Computational, Fluid, Thermal


Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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15 May 2019 Manuscript

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Manuscripts can be submitted to this Research Topic via the following journals:

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Submission Deadlines

15 May 2019 Manuscript

Participating Journals

Manuscripts can be submitted to this Research Topic via the following journals:

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