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The macros listed in Table 3.2.20- 3.2.23 can be used to return real face variables in SI units. They are identified by the F_ prefix. Note that these variables are available only in the pressure-based solver. In addition, quantities that are returned are available only if the corresponding physical model is active. For example, species mass fraction is available only if species transport has been enabled in the Species Model dialog box in ANSYS FLUENT. Definitions for these macros can be found in the referenced header files (e.g., mem.h).
Face Centroid (
F_CENTROID)
The macro listed in Table 3.2.20 can be used to obtain the real centroid of a face. F_CENTROID finds the coordinate position of the centroid of the face f and stores the coordinates in the x array. Note that the x array is always one-dimensional, but it can be x[2] or x[3] depending on whether you are using the 2D or 3D solver.
The ND_ND macro returns 2 or 3 in 2D and 3D cases, respectively, as defined in Section 3.4.2. Section 2.3.15 contains an example of F_CENTROID usage.
Face Area Vector (
F_AREA)
F_AREA can be used to return the real face area vector (or `face area normal') of a given face f in a face thread t. See Section 2.7.3 for an example UDF that utilizes F_AREA.
By convention in ANSYS FLUENT, boundary face area normals always point out of the domain. ANSYS FLUENT determines the direction of the face area normals for interior faces by applying the right hand rule to the nodes on a face, in order of increasing node number. This is shown in Figure 3.2.1.
ANSYS FLUENT assigns adjacent cells to an interior face ( c0 and c1) according to the following convention: the cell out of which a face area normal is pointing is designated as cell C0, while the cell in to which a face area normal is pointing is cell c1 (Figure 3.2.1). In other words, face area normals always point from cell c0 to cell c1.
Flow Variable Macros for Boundary Faces
The macros listed in Table 3.2.22 access flow variables at a boundary face.
Crucially, the Gandharan Buddha is not an ordinary human. Fisher points to the lakshanas (32 marks of a great man) that adorn the figure: the urna (hairless dot between the eyebrows, symbolizing the third eye of spiritual vision), the ushnisha (cranial bump, representing wisdom), and the mudras (hand gestures). For example, the bhumisparsha mudra (earth-touching gesture) commemorates the moment the Buddha called the earth to witness his right to enlightenment. By representing the Buddha in this codified manner, Gandharan art created a visual vocabulary that transcended language. The human form became a mirror for the practitioner: you too can achieve this state . Fisher asserts that this “idealized realism” is the genius of Mahayana Buddhism, making the distant goal of Buddhahood seem attainable. In the later Vajrayana (Tantric) traditions of Tibet and East Asia, Fisher shows how architecture evolves into a fully realized mandala. The quintessential example is the Buddhist temple or chaitya hall , often designed as a square courtyard with a central image. The square represents the physical world (earth), while the circle represents the perfection of enlightenment (heaven). The entrance is typically oriented to the east, the direction of rebirth and renewal.
Fisher emphasizes that circumambulation ( pradakshina )—walking clockwise around the stupa—is an act of meditation. The pilgrim’s path mirrors the cycle of birth, death, and rebirth ( samsara ), while the destination at the top of the stupa symbolizes release. Similarly, other aniconic symbols—the Bodhi tree (enlightenment), the Dharma wheel (the Buddha’s first sermon), and the footprints (the Buddha’s absent presence)—function as teaching devices. They compel the viewer to contemplate the idea of the Buddha rather than worship his personality. As Fisher notes, this “emptiness” of form is perfectly aligned with the Buddhist doctrine of anatman (no-self). One of Fisher’s most insightful chapters concerns the shift to anthropomorphic representations of the Buddha in the region of Gandhara (modern-day Pakistan/Afghanistan) around the 1st century CE. Influenced by Greco-Roman art, Gandharan sculptors began carving the Buddha in human form, complete with wavy hair, realistic robes, and a youthful, serene face. Critics might see this as a departure from the aniconic principle, but Fisher argues it is a natural evolution. The human Buddha became a narrative tool—a way to depict the Jataka tales (stories of the Buddha’s previous lives) and the historical events of his life: his birth, renunciation, enlightenment, and final parinirvana . buddhist art and architecture robert e fisher pdf
The pagoda of China and Japan, a multistoried tower derived from the Indian stupa, is another architectural mandala. Each story corresponds to a stage of consciousness or a cosmic realm. Climbing the pagoda is a physical metaphor for ascending through the dhyanas (states of meditative absorption). Similarly, the mandala itself—a geometric diagram painted on cloth or carved in stone—is a “virtual temple.” Fisher explains that when a monk visualizes the mandala during meditation, he is mentally entering the palace of a Buddha, deconstructing his ego, and reconstructing his mind as a pure land. The famous Borobudur in Java is perhaps the ultimate expression of this principle: a massive stupa-temple structured as a three-dimensional mandala, guiding pilgrims through the realms of desire, form, and formlessness. Robert E. Fisher’s enduring contribution is his insistence that Buddhist art and architecture are not static objects of beauty but dynamic vehicles for spiritual transformation. Whether it is the silent, aniconic stupa, the serene human Buddha of Gandhara, or the complex cosmic mandala of Tibet, each form serves the same function: to anchor abstract philosophy in concrete experience. The layperson sees a story; the practitioner sees a path; the enlightened sees a mirror of their own mind. Crucially, the Gandharan Buddha is not an ordinary human
Based on the foundational principles of Robert E. Fisher’s Buddhist Art and Architecture Introduction Buddhist art and architecture are not merely decorative or functional; they are tangible expressions of a philosophical quest. In his seminal work, Buddhist Art and Architecture , Robert E. Fisher argues that to understand these visual forms is to understand Buddhism itself. Unlike the art of many other religions, which often celebrates divine miracles or historical conquests, Buddhist art serves a single, profound purpose: to act as a visual guide on the path to enlightenment (nirvana). From the mound-like stupa to the meditative Buddha statue, every element is encoded with meaning. This essay explores Fisher’s core thesis—that Buddhist art and architecture function as a mandala , a symbolic map of the cosmos and the mind—by examining three key developments: the aniconic phase of early Buddhism, the anthropomorphic revolution of the Gandharan school, and the cosmic architecture of the Buddhist temple. The Stupa and the Aniconic Symbolism (The Early Phase) As Fisher meticulously details, the earliest Buddhist art (circa 3rd century BCE) avoided depicting the historical Buddha, Siddhartha Gautama, in human form. Instead, artists used aniconic (non-human) symbols. The most important of these is the stupa —a dome-shaped mound containing relics of the Buddha or his disciples. The stupa is not a tomb but a three-dimensional mandala. Its hemispherical dome represents the dome of heaven enclosing the earth; the central spire (the yasti ) symbolizes the cosmic axis connecting heaven and earth; and the umbrella-like discs ( chattra ) represent the three jewels of Buddhism: the Buddha, the Dharma (teachings), and the Sangha (community). By representing the Buddha in this codified manner,
See Section 2.7.3 for an example UDF that utilizes some of these macros.
Flow Variable Macros at Interior and Boundary Faces
The macros listed in Table 3.2.23 access flow variables at interior faces and boundary faces.
| Macro | Argument Types | Returns |
| F_P(f,t) | face_t f, Thread *t, | pressure |
| F_FLUX(f,t) | face_t f, Thread *t | mass flow rate through a face |
F_FLUX can be used to return the real scalar mass flow rate through a given face f in a face thread t. The sign of F_FLUX that is computed by the ANSYS FLUENT solver is positive if the flow direction is the same as the face area normal direction (as determined by F_AREA - see Section 3.2.4), and is negative if the flow direction and the face area normal directions are opposite. In other words, the flux is positive if the flow is out of the domain, and is negative if the flow is in to the domain.
Note that the sign of the flux that is computed by the solver is opposite to that which is reported in the ANSYS FLUENT GUI (e.g., the Flux Reports dialog box).
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3.2.3 Cell Macros
